Question: Why do Mormons Have Another Book? In the Doctrine and Covenants (A sacred text in The Church of Jesus Christ of Latter-day Saints) it states that the Bible AND the Book of Mormon contain the "fulness of the gospel". If the Bible contains the "fulness of the gospel," then why do they need the Book of Mormon?
And again, the elders, priests and teachers of this church shall teach the principles of my gospel, which are in the Bible and the Book of Mormon, in the which is the fulness of the gospel. [Emphasis added]
You interpreted this as meaning that the Bible
and the Book of Mormon individually contain the fulness of the gospel as opposed to the Bible and Book of Mormon collectively containing the fulness of the gospel. In actuality both statements are correct, but to answer your question we'll use the first interpretation (individually containing the fulness).
In order to understand this verse we need to understand what is meant by the term "fulness of the gospel." My favorite explanation of this term is provided by Joseph Fielding McConkie in the book "Revelations of the Restoration":
"In saying that the Book of Mormon contains "the fulness of the gospel," what is meant is that it contains those fundamental truths upon which all saving principles must build. These are the principles one should understand before baptism. To be baptized we need not understand all there is to know about the gospel. We simply need to have laid a foundation of faith and understanding upon which we can continue to build until we have received a fulness of all that the Father has."
The Book of Mormon serves as another testament of the divine mission of Jesus Christ. If you come to know the Book of Mormon is true through reading and pondering its message, then praying about it's truthfulness and receiving an affirmative answer, you simultaneously accept two truths:
1. Jesus Christ is really the savior of mankind and the Bible is a true record of his dealings with those of the old world—because the Book of Mormon supports the Bible's history.
2. Joseph Smith was really a prophet of God and hence his teachings are true.
"But I already believe the Bible is true and that God is real, why does it matter if the Book of Mormon is true?"
Though the Bible contains the fundamental truths upon which saving principles must build, there is much of God's eternal plan that we cannot hope to understand solely through the Bible. Not only does the Book of Mormon strengthen the foundation of our understanding of the gospel of Jesus Christ, but other truths brought forth by the Prophet Joseph Smith build upon this foundational understanding and fill in the details of where we came from, why we're here and where we're going.
Haven't you wondered what existence consisted of before you were born? Wouldn't you want to know if you are really living in harmony with God's will? Don't you want to know what people really do in heaven, or do you just think they just sit there in a robe and play the harp all day?
I hope that answers why the Book of Mormon is needed and why it is so important to those who believe in its message.
Head over to mormon.org to learn more.