See the shaded stone? That's the keystone of the arch - the bit holding it all together.
If an archway was built without a keystone ... bam. Goodbye arch.
The reason we Mormons call the Book of Mormon the keystone of our religion, is because without it, our religion crumbles. It is the most important part, holding up the remainder of our beliefs.
(Incidentally, that is the ideal way to know if what we belief is true or not. Read the Book of Mormon, and make your own mind up.)
Toward the end of the introduction to the Book of Mormon, it says:
"Concerning this record the Prophet Joseph Smith said: “I told the brethren that the Book of Mormon was the most correct of any book on earth, and the keystone of our religion, and a man would get nearer to God by abiding by its precepts, than by any other book.” "
The prophet at the time, Joseph Smith, compared the Book of Mormon to a keystone because this book is crucial to the restored gospel of Jesus Christ, and it influences our testimony (our belief) of other aspects of the gospel of Jesus Christ.
The introduction continues:
"We invite all men everywhere to read the Book of Mormon, to ponder in their hearts the message it contains, and then to ask God, the Eternal Father, in the name of Christ if the book is true. Those who pursue this course and ask in faith will gain a testimony of its truth and divinity by the power of the Holy Ghost. (See Moroni 10:3–5.)
Those who gain this divine witness from the Holy Spirit will also come to know by the same power that Jesus Christ is the Savior of the world, that Joseph Smith is his revelator and prophet in these last days, and that The Church of Jesus Christ of Latter-day Saints is the Lord’s kingdom once again established on the earth, preparatory to the second coming of the Messiah."
Some may gain a testimony or firm belief in another stone first - that the Atonement of Jesus Christ is very real, or that God calls prophets today just as He did in the day of Moses or Noah. It all adds up. Gaining a testimony of the Book of Mormon will help people know that Joseph Smith was a true prophet of God.
And that The Church of Jesus Christ of Latter-day Saints is true.