In the Chapter 20 Book of the Apocalypse there is a passage referring to Satan being bound for 1,000 years, and that those who refuse the mark of the Beast shall reign with Christ for 1,000 years.
" [2] And he laid hold on the dragon the old serpent, which is the devil and Satan, and bound him for a thousand years. [3] And he cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should no more seduce the nations, till the thousand years be finished. And after that, he must be loosed a little time. [4] And I saw seats; and they sat upon them; and judgement was given unto them; and the souls of them that were beheaded for the testimony of Jesus, and for the word of God, and who had not adored the beast nor his image, nor received his character on their foreheads, or in their hands; and they lived and reigned with Christ a thousand years. [5] The rest of the dead lived not, till the thousand years were finished. This is the first resurrection.[6] Blessed and holy is he that hath part in the first resurrection. In these the second death hath no power; but they shall be priests of God and of Christ; and shall reign with him a thousand years."
I shall FIRST concentrate on authentic official Roman Catholic teaching.
According to the Douay-Rheims Bible - this is the Church's official interpretation:
"Bound him": The power of Satan has been very much limited by the passion of Christ: for a thousand years; that is, for the whole time of the New Testament; but especially from the time of the destruction of Babylon or pagan Rome, till the new efforts of Gog and Magog against the church, towards the end of the world. During which time the souls of the martyrs and saints live and reign with Christ in heaven, in the first resurrection, which is that of the soul to the life of glory; as the second resurrection will be that of the body, at the day of the general judgement.
This passage shows the Church teaches the "1,000 years" of binding of Satan began with the Passion of Christ on the Cross when His Blood bound up his demonic power. The Church was then established, and this began the LAST AGE of the earth. Notice how the teaching says this will last until the efforts of Gog and Magog come against the Church at the END OF THE WORLD - that this '1,000 years' means until the attack of the Antichrist. Since we're well over a literal 1,000 years, this shows that the Church has interpreted this "1,000 years" a symbolic number representing the foundation of the Church which ushered in the Last Age of the earth. The number '1,000' will end with the arrival of the Antichrist, who Christ Himself will defeat before the General Judgement, aka the Second Resurrection.
The Douay-Rheims Bible then tells us that this is what is meant by the 'First Resurrection' and "reigning with Christ for 1,000 years" - the souls of the saints and martyrs who died since the time of the founding of the Church are enjoying thrones in Heaven and reigning with Christ in Heaven as the doors of Heaven are now opened to us when before His death and Ascension they were closed. The opening of these doors is the First Resurrection. The symbolic 1,000 years ends with the the Second Resurrection, which refers to the Second Coming, the General Judgement and the entrance of the New Heaven and New Earth. The 'Second Death' refers to Hell since the phrase 'the first death' is a reference to physical death - the 'second' is eternal death for those who are damned.
So, to recap, the "1,000 years" ACCORDING TO OFFICIAL AND AUTHENTIC CHURCH TEACHING as explained in the traditional Douay-Rheims Bible is SYMBOLIC and represents the period of time starting from when Christ's Blood bound up the power of the demons when He died on the Cross, the Gates of Heaven were opened and the Church was founded - it will end at the General Judgement and the End of Time. The number is NOT literal.
What about the 'Mark of the Beast'? Note it doesn't only refer to the Antichrist at the end times attempting to physically mark everyone - the devil with his antichrist precursors has always tried to mark his own from the beginning. St. John the Evangelist warned there would always be antichrist precursors. The early Christians noted the number "666" in number cyphers also spelled out "NERO" - and they recognised him as a servant of if not the literal antichrist. So, Christians have always had to refuse the "Mark of the Beast" since the time the Church was founded - the mark is spiritual as well as physical. Those who refuse to follow Satan and the ways of the world and follow their Catholic faith are usually persecuted and are in extreme cases denied from having careers, or, life is generally made hard, even to the point of martyrdom, etc. there is a suffering involved in remaining detached from the evils of the world, which as we see today, is growing stronger, and will is literally going to happen to those who will be physically marked by the Antichrist in the end times.
Now, here is the false interpretation of the year 1,000 - mainly, that Christ will come back and literally reign 1,000 years before the Day of Judgement. This interpretation has been entertained since early times, mostly among heretics, and was and has been recognized by the Church to be a Gnostic belief contrary to authentic Church teachings. The chiliast heresy was also taken up by the Montanist schismatics.
It took awhile to curb the spread of this error, great theologians such as Origen of Alexandria, St. Augustine and St. Jerome eventually showed that there is no literal millennium going to occur, it was a spiritual analogy.
Of interest, the "New Advent" site notes that during the Medieval period while there was a hope for the great revival of Christianity, especially through the growing belief that the renewal would happen through the 'holy emperor' as stated in the early prophecies of the Church Fathers - hope in these prophecies did NOT have the chiliast heresy in them. It was the PROTESTANTS who started to spread the chiliast concept of a literal 1,000 year reign again. (See the "New Advent" article, click here.)