The belief that the millennium of Revelation 20:1-7 refers to a time of fullness such as the current Church age and not to a literal one-thousand-year period of time. While amillennialists disagree about what the millennium is or will be, they do agree it will not be a future, earthly reign of Christ.
Amillennialism (from the Latin prefix a meaning "no," mille meaning "thousand," and annum meaning "year") is a view in Christian eschatology named for its denial of a future, thousand-year, physical reign of Jesus Christ on the earth, as espoused in the premillennial and some postmillennial views of the Book of Revelation, http://www.biblegateway.com/passage/?search=rev+20 chapter 20. By contrast, the amillennial view holds that the number of years in Revelation 20 is a symbolic number, not a literal description; that the millennium has already begun and is identical with the church age (or more rarely, that it ended with the destruction of Jerusalem in AD 70); and that while Christ's reign is spiritual in nature during the millennium, at the end of the church age, Christ will return in final judgement and establish permanent physical reign.