The Will of the divine Testator is this: It is incumbent upon the Aghsan, the Afnan and My Kindred to turn, one and all, their faces towards the Most Mighty Branch. Consider that which We have revealed in Our Most Holy Book: ‘When the ocean of My presence hath ebbed and the Book of My Revelation is ended, turn your faces toward Him Whom God hath purposed, Who hath branched from this Ancient Root.’ The object of this sacred verse is none other except the Most Mighty Branch [Abdu’l-Bahá]. Thus have We graciously revealed unto you Our potent Will, and I am verily the Gracious, the All-Powerful. Verily God hath ordained the station of the Greater Branch [Muhammad Ali] to be beneath that of the Most Great Branch [Abdu’l-Bahá]. He is in truth the Ordainer, the All-Wise. We have chosen ‘the Greater’ after ‘the Most Great’, as decreed by Him Who is the All-Knowing, the All-Informed.
Bahá’u'lláh, The Kitab-i-Ahd (Book of My Covenant), paragraph 9

O people of the world! When the Mystic Dove will have winged its flight from its Sanctuary of Praise and sought its far-off goal, its hidden habitation, refer ye whatsoever ye understand not in the Book to Him Who hath branched from this mighty Stock.
Bahá’u’lláh, The Kitab-i-Aqdas, paragraph 174

Six days before [Bahá'u'lláh] passed away He summoned to His presence, as He lay in bed leaning against one of His sons, the entire company of believers, including several pilgrims, who had assembled in the Mansion, for what proved to be their last audience with Him. “I am well pleased with you all,” He gently and affectionately addressed the weeping crowd that gathered about Him. “Ye have rendered many services, and been very assiduous in your labors. Ye have come here every morning and every evening. May God assist you to remain united. May He aid you to exalt the Cause of the Lord of being.” To the women, including members of His own family, gathered at His bedside, He addressed similar words of encouragement, definitely assuring them that in a document entrusted by Him to the Most Great Branch ['Abdu'l-Bahá] He had commended them all to His care.
Shoghi Effendi, God Passes By p.222

There hath branched from the Sadratu’l-Muntahá this sacred and glorious Being, this Branch of Holiness; well is it with him that hath sought His shelter and abideth beneath His shadow. Verily the Limb of the Law of God hath sprung forth from this Root which God hath firmly implanted in the Ground of His Will, and Whose Branch hath been so uplifted as to encompass the whole of creation. Magnified be He, therefore, for this sublime, this blessed, this mighty, this exalted Handiwork!… A Word hath, as a token of Our grace, gone forth from the Most Great Tablet—a Word which God hath adorned with the ornament of His own Self, and made it sovereign over the earth and all that is therein, and a sign of His greatness and power among its people …Render thanks unto God, O people, for His appearance; for verily He is the most great Favor unto you, the most perfect bounty upon you; and through Him every mouldering bone is quickened. Whoso turneth towards Him hath turned towards God, and whoso turneth away from Him hath turned away from My beauty, hath repudiated My Proof, and transgressed against Me. He is the Trust of God amongst you, His charge within you, His manifestation unto you and His appearance among His favored servants… We have sent Him down in the form of a human temple. Blest and sanctified be God Who createth whatsoever He willeth through His inviolable, His infallible decree. They who deprive themselves of the shadow of the Branch, are lost in the wilderness of error, are consumed by the heat of worldly desires, and are of those who will assuredly perish.

Bahá’u’lláh - Tablet of the Branch cited in The Dispensation of Bahá’u’lláh, paragraph 78

To direct and canalize these forces let loose by this Heaven-sent process, and to insure their harmonious and continuous operation after His ascension, an instrument divinely ordained, invested with indisputable authority, organically linked with the Author of the Revelation Himself, was clearly indispensable. That instrument Bahá’u’lláh had expressly provided through the institution of the Covenant, an institution which He had firmly established prior to His ascension. This same Covenant He had anticipated in His Kitáb-i-Aqdas, had alluded to it as He bade His last farewell to the members of His family, who had been summoned to His bed-side, in the days immediately preceding His ascension, and had incorporated it in a special document which He designated as “the Book of My Covenant,” and which He entrusted, during His last illness, to His eldest son ‘Abdu’l-Bahá.

Written entirely in His own hand; unsealed, on the ninth day after His ascension in the presence of nine witnesses chosen from amongst His companions and members of His Family; read subsequently, on the afternoon of that same day, before a large company assembled in His Most Holy Tomb, including His sons, some of the Báb’s kinsmen, pilgrims and resident believers, this unique and epoch-making Document, designated by Bahá’u’lláh as His “Most Great Tablet,” and alluded to by Him as the “Crimson Book” in His “Epistle to the Son of the Wolf,” can find no parallel in the Scriptures of any previous Dispensation, not excluding that of the Báb Himself. For nowhere in the books pertaining to any of the world’s religious systems, not even among the writings of the Author of the Bábí Revelation, do we find any single document establishing a Covenant endowed with an authority comparable to the Covenant which Bahá’u’lláh had Himself instituted.
Shoghi Effendi, God Passes By, p. 237-8

“O Thou Who art the apple of Mine eye!” Bahá’u’lláh, in His own handwriting, thus addresses ‘Abdu’l-Bahá, “My glory, the ocean of My loving-kindness, the sun of My bounty, the heaven of My mercy rest upon Thee. We pray God to illumine the world through Thy knowledge and wisdom, to ordain for Thee that which will gladden Thine heart and impart consolation to Thine eyes.” “The glory of God rest upon Thee,” He writes in another Tablet, “and upon whosoever serveth Thee and circleth around Thee. Woe, great woe, betide him that opposeth and injureth Thee. Well is it with him that sweareth fealty to Thee; the fire of hell torment him who is Thine enemy.” “We have made Thee a shelter for all mankind,” He, in yet another Tablet, affirms, “a shield unto all who are in heaven and on earth, a stronghold for whosoever hath believed in God, the Incomparable, the All-Knowing. God grant that through Thee He may protect them, may enrich and sustain them, that He may inspire Thee with that which shall be a wellspring of wealth unto all created things, an ocean of bounty unto all men, and the dayspring of mercy unto all peoples.”

Shoghi Effendi, The Dispensation of Bahá’u’lláh, paragraph 79

In a letter dictated by Bahá’u’lláh and addressed by Mírzá Áqá Ján, His amanuensis, to ‘Abdu’l-Bahá while the latter was on a visit to Beirut, we read the following: “Praise be to Him Who hath honored the Land of Bá (Beirut) through the presence of Him round Whom all names revolve. All the atoms of the earth have announced unto all created things that from behind the gate of the Prison-city there hath appeared and above its horizon there hath shone forth the Orb of the beauty of the great, the Most Mighty Branch of God—His ancient and immutable Mystery—proceeding on its way to another land. Sorrow, thereby, hath enveloped this Prison-city, whilst another land rejoiceth… Blessed, doubly blessed, is the ground which His footsteps have trodden, the eye that hath been cheered by the beauty of His countenance, the ear that hath been honored by hearkening to His call, the heart that hath tasted the sweetness of His love, the breast that hath dilated through His remembrance, the pen that hath voiced His praise, the scroll that hath borne the testimony of His writings.”

Shoghi Effendi, World Order of Bahá’u’lláh, p. 136

In accordance with the explicit text of the Kitáb-i-Aqdas Bahá’u'lláh hath made the Center of the Covenant the Interpreter of His Word - a Covenant so firm and mighty that from the beginning of time until the present day no religious Dispensation hath produced its like.
‘Abdu’l-Bahá, cited in The World Order of Bahá’u'lláh p. 136

Today, the most important affair is firmness in the Covenant, because firmness in the Covenant wards off differences. ….Bahá’u'lláh covenanted, not that I (’Abdu’l-Bahá) am the Promised One, but that ‘Abdu’l-Bahá is the Expounder of the Book and the Centre of His Covenant, and that the Promised One of Bahá’u'lláh will appear after one thousand or thousands of years. This is the Covenant which Bahá’u'lláh made. If a person shall deviate, he is not acceptable at the Threshold of Bahá’u'lláh. In case of differences, ‘Abdu’l-Bahá must be consulted. They must revolve around his good pleasure. After ‘Abdu’l-Bahá, whenever the Universal House of Justice is organized it will ward off differences.
‘Abdu’l-Bahá, cited in “Star of the West”, vol. 4, No. 14 (November 1913), p. 237-38

…to a true Bahá’í who is steadfast in the Covenant, obedience to the utterances of ‘Abdu’l-Bahá is obedience to God. Recognition of the station of Bahá’u'lláh and believing in Him, important as they are, will not be a sufficient guarantee of one’s faith unless one remains loyal and steadfast in His Covenant. One of the distinguishing features of the Faith of Bahá’u'lláh is that He has not abandoned His followers to their own devices. He has left in their midst a source of divine guidance to which they can turn. He conferred His divine powers and authority upon ‘Abdu’l-Bahá and made a firm covenant with the believers to follow and obey Him with absolute devotion and love. This covenant was extended to include Shoghi Effendi and the Universal House of Justice. Therefore faith in Bahá’u'lláh is not a mere acknowledgement of His divine message, but involves, in addition, obedience and faithfulness to those upon whom He has conferred the mantle of infallibility.
Adib Taherzadeh, The Covenant of Bahá’u’lláh, p. 266

Why didn’t Bahá’u’lláh announce the appointment of Abdu’l-Baha during His lifetime?

That the identity of the Centre of the Covenant was kept secret and revealed only after the ascension of Bahá’u'lláh constitutes one of the most important features of the Covenant. A deeper understanding of this Covenant depends upon the individual appreciating the manifold wisdoms hidden in this act of Bahá’u'lláh. Not until one grasps the purpose and significance of such secrecy in the appointment of the successor, be he ‘Abdu’l-Bahá, Shoghi Effendi, or the Universal House of Justice, will the believer be able to acquire a true comprehension of the Covenant of Bahá’u'lláh in all its aspects.

Although such an understanding must come about primarily through the believer himself meditating upon the Holy Writings, studying the history of the Covenant, its genesis, and its workings, and praying that his heart may become the recipient of divine knowledge, yet the following explanation may throw some light on this important subject.

The main function of the Manifestation of God is to reveal the teachings of God for the age in which He appears. In so doing, He is ready to explain to His followers the meaning and purpose of His Revelation and to solve any difficult questions for them. Both in His association with the believers and in His Tablets, Bahá’u'lláh was always ready to explain the significances which were enshrined in His Writings. Many of His Tablets were revealed in response to the various questions which were asked by His followers and, at times, by others. These questions ranged from weighty religious and spiritual matters to unimportant minor problems which affected the lives and activities of the friends. To all these questions Bahá’u'lláh responded by expounding His teachings, interpreting the Scriptures of the past, clarifying many of their abstruse passages and statements, revealing the mysteries surrounding some of His profound utterances, delineating the features of His New World Order, giving details of the application of His laws and ordinances, and explaining, in simple terms, the verities of His Faith to those who requested further elucidation.

However, on one subject Bahá’u'lláh remained silent: designating the person who was to succeed Him. There are many wisdoms in this. Let us return yet again to the analogy of the teacher. It is the teacher’s duty to impart knowledge to his pupils and help them in their work, and he is always ready to explain the various subjects to his pupils and answer their questions. But on one occasion he must remain silent and refrain from helping them or answering their questions: namely, on the examination day. On that day the students are left on their own and will have to find the answers by themselves. Only those who pass the examinations are elevated to a higher class, and those who fail are not.
Adib Taherzadeh, The Covenant of Bahá’u’lláh, p. 144