What is known as "The Golden Plates" is a record of a people in the Ancient Americas, engraved into metal plates, which Joseph Smith translated in the 1800's to become The Book of Mormon: Another Testament of Jesus Christ. Many ancient prophets contributed to this record of Christ's visit to the Americas and the events leading up to it. The Book of Mormon is not a replacement for the Bible, but a companion to the Bible with the express purpose of testifying of Jesus Christ. For more information see mormon.org.
If you are not Mormon, this probably seems to be a preposterous story. Members of the The Church of Jesus Christ of Latter-day Saints are not asked to take anyone else's word for it, but are expected to find out for themselves if it's true. Joseph Smith's sincere search for truth, as a fourteen-year-old boy, prompted by this Bible verse, "If any of you lack wisdom, let him ask of God, that giveth to all men liberally, and upbraideth not, and it shall be given him," (James 1:5) led him to the woods near his home to pray and find out for himself which church was right. That led to his vision of God the Father and his Son Jesus Christ and eventually the establishment of The Church of Jesus Christ of Latter-day Saints.
Moroni, a Book of Mormon prophet, makes this promise, "And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost." Moroni 10:4
When someone has found out for him/herself that these teachings are true, it is called a "testimony." Sharing these feelings with others is called "bearing your testimony." Each person's testimony is unique and personal.