The millennium (from the Latin 'mille' meaning 'thousand') is the period of 1,000 years when Christ rules on earth, referred to in a number of Scriptures; one of the most obvious being in the book of Revelation:

1 I saw an angel coming down out of Heaven, having the key of the abyss and a great chain in his hand.
2 He laid hold on the dragon, the old serpent, which is the Devil and Satan, and bound him for one thousand years,
3 and cast him into the abyss, and shut it, and sealed it over him, that he should deceive the nations no more, until the thousand years are finished. After this, he must be freed for a little time.
4 I saw thrones, and they sat on them, and judgment was given to them. I saw the souls of those who had been beheaded for the testimony of Jesus, and for the word of God, and such as didn't worship the beast nor his image, and didn't receive the mark on their forehead and on their hand. They lived, and reigned with Christ one thousand years.
5 The rest of the dead didn't live until the thousand years were finished. This is the first resurrection.
Rev. 20:1-5