A millennium is a period of 1,000 years. When we speak of "the Millennium," we refer to the 1,000 years following the Savior's Second Coming (see Revelation 20:4; D&C 29:11). During the Millennium, "Christ will reign personally upon the earth" (Articles of Faith 1:10).
The Millennium will be a time of righteousness and peace on the earth. The Lord has revealed that "in that day the enmity of man, and the enmity of beasts, yea, the enmity of all flesh, shall cease" (D&C 101:26; see also Isaiah 11:6-9). Satan will be "bound, that he shall have no place in the hearts of the children of men" (D&C 45:55; see also Revelation 20:1-3).
During the Millennium, all people on the earth will be good and just, but many will not have received the fulness of the gospel. Consequently, members of the Church will participate in missionary work.
Members of the Church will also participate in temple work during the Millennium. The Saints will continue to build temples and receive ordinances in behalf of their kindred dead. Guided by revelation, they will prepare records of their ancestors all the way back to Adam and Eve.
Complete righteousness and peace will continue until the end of the 1,000 years, when Satan "shall be loosed for a little season, that he may gather together his armies." The armies of Satan will fight against the hosts of heaven, who will be led by Michael, or Adam. Satan and his followers will be defeated and cast out forever. (See D&C 88:111-115.)