Plural marriage, more commonly called polygamy, was an early LDS practice in which some men had more than one living wife. Joseph Smith introduced it in the 1840s as part of what he called the new and everlasting covenant (Doctrine and Covenants 132), teaching that it was commanded by God and tied to exaltation.
The practice expanded under Brigham Young in Utah but was officially discontinued in 1890 under U.S. government pressure. Today, the LDS Church rejects polygamy and excommunicates members who attempt it. However, the doctrine remains in their scripture (D&C 132), and many Mormons believe plural marriage will continue in the celestial kingdom. Breakaway fundamentalist groups still practice it.