Our Church was founded by Joseph Smith, Jr. He lived in New York state during the period which came to be called "The Great Awakening." As a boy, he believed in God and asked Him which of the many competing Churches to join as the Scriptures instruct.

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.
King James Version of the Bible, James 1:5

He was told to join none of them at that time. He continued asking God about the true church for years and, later, he was instructed to reestablish the Church on earth.

The members of the Church called themselves "Latter Day Saints" to identify with the New Testament Christians whose faith they felt had been restored by God; another name they called themselves was "Restorationists." They were labeled "Mormons" because they accepted The Book of Mormon as a second book of Scripture, complementary the Bible. The name "Mormons" was meant to be an insult and a means of denigration.

The founder of our Church was killed by an angry mob while he was in custody in a jail in Carthage, Illinois. One of the Church leaders at that time, Apostle Brigham Young, asserted that he should lead the Church and led a group of Saints out of the United States. They started the community that would become Salt Lake City, Utah. They would become the Church of Jesus Christ of Latter Day Saints (LDS).

Under the leadership of President Young and his successors, the LDS adopted many new beliefs and practices which had been speculated about and discussed before the Church had been driven from their homes in Nauvoo, Illinois. The ideas underlying these new beliefs and practices came from several places, but many of the ideas which became important came from Freemasonry and from other Utopian religious communities as members from those groups joined with the Saints.  The adoption of these highly speculative ideas completely transformed the beliefs, church structure, and practices of the LDS.

Meanwhile, a remnant of the Church remained in their homes, continued to worship as they had been, and waited for God to raise up a new President/Prophet. Eventually Joseph Smith III accepted the call to leadership of the faithful remnant. The remnant Saints reorganized the Church under his leadership and became the Reorganized Church of Jesus Christ of Latter Day Saints (RLDS).

In a lawsuit to settle which Church (RLDS or LDS) owned the land that the original Latter Day Saints had held in the Independence area, even the Court held the RLDS was the closer successor to the beliefs and practices of the parent Church.

Anyway, that's the "Reader's Digest condensed version" of RLDS history. The complete story is much longer and more complex. It is the story of thousands of individuals diligently searching for God and for understanding about His desires for the people of our world and time.