"Millennium" comes from the Latin mille (thousand) and annum (year). Revelation 20:4 mentions a thousand-year period which is usually called the millennium. In speaking of the saints, Revelation 20:4 says "they came to life and they reigned with Christ for a thousand years."
Based on this passage many people have taught that, after the Second Coming, Christ will reign on Earth for a thousand years. The belief Christ will come before the millennium is called premillennialism. Many television preachers are premillennialists.
Other Christians hold that the millennium is not a literal thousand-year period, but a figurative one used to refer to the time in which Christ reigns on earth through his Church. This time has not yet come.
Some who accept this view believe the world will get better under Christian influence and that there will be a time when society as a whole will be Christianized. This is their version of the millennium.
In this view, Christ will return after the millennium to judge the living and the dead. This idea is called postmillennialism.
There are also those who believe the millennium is symbolic of the entire age of the Church. They point to Bible verses which speak of Christ reigning in heaven now. This is called amillennialism (no millennium), although some prefer to called it realized millennialism because it doesn't deny the millennium, but merely interprets it as a symbol of the Church age.
The Catholic Church has never defined which position is correct. Still, most Catholic theologians have been amillennialists or postmillennialists. We can't think of any who have been premillennialists.