After Joseph Smith was called to be a Prophet and restore Christ's Church to the Earth, God knew that many would not believe his claim to have seen a vision and or to have been called of God. It was wisdom in God to provide proof of his Joseph's divine calling. The evidence that he gave Joseph was the Book of Mormon.
The Book of Mormon actually starts out in Jerusalem about 600 years before Christ. There was a man named Lehi living there with his family. Lehi was a prophet of God proclaiming repentace just as all prophets do, and experienced much rejection due to the wickedness of the people. His life was in danger and so God commanded that he take his family and travel into the wilderness. His youngest son Nephi makes a kind of journal out of golden plates. It goes on to give a history of Lehi and his people for about 1,000 years. In that history is contained many trials and tribulations that the people went through and also their dealings with God and many revealations. The record was past down from generation to generation each prophet gives an accounting of there teachings and dealings with God. About 400 years after the death of Christ, the people were getting so wicked that they were at war with one another and all of the righteous had been slain except for one man, his name was Moroni. He witnessed the distruction of his entire nation because of wickedness and now he was alone and was in danger constantly of being hunted by his enemies and being destroyed. It was his duty to keep the plates safe from the hands of his wicked enemies. After he had given a record of him and his people he was commanded by God to bury the record in the earth so that it would be preserved.
In the Bible, Christ says that we can know if a prophet is true or not through the fruits that he brings forth. The Book of Mormon is the fruit of the Prophet Joseph Smith. No he did not write the Book of Mormon, but we can know if Joseph Smith was really called of God, when we come to know that the Book is true. He translated it only having a 3rd graders education. If it is true, he translated it correctly and we can know that he truly was directed by God.