You can read their detailed story HERE.
In a nutshell, as Restornu implied HERE with her children of LDS General Authorities comment, the Tanners have a blue chip LDS pedigree. Sandra is a direct descendant of Brigham Young and Gerald is a direct descendant of Nathan Tanner (who played a large part in bankrolling the Mormon Church in the days of Joseph Smith). To quote an analogy from U.S. history, it is as though she were the great granddaughter of Thomas Jefferson and he were the great grandson of Alexander Hamilton.
As bright people, they began to question some of the obvious errors and inconsistencies of Mormonism. Eventually the cumulative effect of these questions, coupled with the lack of answers from Mormon authorities, led them to dump the church and seek a personal relationship with Christ.
Later, partially out of love for their family members still in the LDS Church and partially out of love for Christ, they began to copy, analyze and then publish documents obtained from the libraries at the University of Utah and BYU.
The Tanners have severely damaged Mormonism -- probably to a greater extent than anyone else has ever wounded any other cult. They have published more than 40 books, and have made thousands of pages of materials available through their WEBSITE. Among other things, they have exploded the story of the First Vision, documented thousands of changes to all of the Standard Works, documented dozens of obvious contradictions in Mormon scripture, published the Temple Ceremony, exposed BH Roberts' charges that Joseph plagiarized the BoM, exposed Joseph's fraudulent translation of the Book of the Book of Abraham, and much, much more.
Today, the Tanners are denigrated as anti-Mormons by members of the LDS Church, and deeply admired and respected by almost everyone else who has taken the time to explore their work.
I encourage every reader of this thread to examine their research in detail, paying particular attention to their annotated sources, and then form your own opinion of the validity Gerald and Sandra Tanner's work.
Thanks for the brief history; I’ve bookmarked their website and will be reading through it as time allows.