Why did God give us prophecy?
God gave us prophecy so that His heart, mind, and will could be made known to His people, both to foretell things to come and to reveal what could never be known by natural means, and so that Christ could be revealed and confirmed to the Church.
Prophecy was given because it is the way God speaks what cannot be discovered through natural means. It declares His heart (how He feels about a thing), His mind (His intent), and His will (what He will do). Much of the prophecy of old was predictive, foretelling events like the birth of Christ in Bethlehem, but prophecy was never only about predicting the future. It was, and is, the speaking forth of the mind and counsel of God to His people.
God also gave prophecy so that a true and reliable witness to Jesus Christ would be present in the earth and in the Church. A prophet's ministry receives a revelation of Jesus Christ, the Church, and the events concerning the Church, and in speaking this out, the prophet confirms the word and revelation of the mystery of Christ that has been given to the apostle. Out of the mouth of two or more witnesses every word is established, so the prophet stands as a witnessing voice alongside the apostle.
Before God established spiritual government in the Church, He used the prophet as the means by which His people still had a word to steer, lead, or guide them, since there was no other order in place. Prophecy also has power toward the unbeliever: when true prophecy goes forth, the secrets of a hearer's heart are made manifest, and he is convinced and judged by it, either falling down to worship God or rejecting the God who has exposed Himself. In this way prophecy manifests a desire to know God or exposes a rejection of Him.
Finally, prophecy is given so that in these last days God speaks to the Church by His Son, no longer only overshadowing single prophets, but desiring to speak through the whole body of the Saints. Even so, prophecy is partial; we know in part and prophesy in part, until that which is perfect is come, so it must be judged and confirmed rather than treated as complete revelation on its own.
The scriptures
But thou, Bethlehem Ephratah, though thou be little among the thousands of Judah, yet out of thee shall he come forth unto me that is to be ruler in Israel; whose goings forth have been from of old, from everlasting.
And one of them, named Caiaphas, being the high priest that same year, said unto them, Ye know nothing at all, Nor consider that it is expedient for us, that one man should die for the people, and that the whole nation perish not. And this spake he not of himself: but being high priest that year, he prophesied that Jesus should die for that nation;
Then the king commanded, and they brought Daniel, and cast him into the den of lions. Now the king spake and said unto Daniel, Thy God whom thou servest continually, he will deliver thee.
Wherefore tongues are for a sign, not to them that believe, but to them that believe not: but prophesying serveth not for them that believe not, but for them which believe. If therefore the whole church be come together into one place, and all speak with tongues, and there come in those that are unlearned, or unbelievers, will they not say that ye are mad? But if all prophesy, and there come in one that believeth not, or one unlearned, he is convinced of all, he is judged of all: And thus are the secrets of his heart made manifest; and so falling down on his face he will worship God, and report that God is in you of a truth.
Charity never faileth: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away. For we know in part, and we prophesy in part. But when that which is perfect is come, then that which is in part shall be done away. When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things. For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.
And God hath set some in the church, first apostles, secondarily prophets, thirdly teachers, after that miracles, then gifts of healings, helps, governments, diversities of tongues.
Of which salvation the prophets have enquired and searched diligently, who prophesied of the grace that should come unto you:
Beloved, believe not every spirit, but try the spirits whether they are of God: because many false prophets are gone out into the world.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.