Why is Satan bound for a thousand years?
Your question comes from a passage of scripture found in the book of Revelation, let's examine the verse in context to see if there is a answer.
Rev 20:1 And I saw an angel come down from heaven, having the key of the bottomless pit and a great chain in his hand.
Rev 20:2 And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years,
Rev 20:3 And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season.
It's important to remember two things when reading the book of Revelation;
1. Whatever interpretation we come up with had to be understandable to the people John was writing to. It makes no sense to have a interpretation so far removed from the time and place of John's audience that what they read would not affect them.
2. Because of persecution the book is full of symbols that would have been understood by John's audience but not by the Roman government.
The apostle John is on the isle of Patmos experiencing one vision after another concerning things pertaining to the church, Jerusalem, and the world at large.
In verse 1 he sees a vision of an angel coming down from heaven with a key and a chain in his hand. We must determine if these are symbolic or if the angel is holding a literal key and chain.
Verse 2 helps us to realize that what we are reading must be symbolic, so what would be the meaning of a key and a chain? Let's determine that first then we'll get to the 1,000 years.
A key is used to lock or unlock something, a chain can be used to restrain, the angel is showing us symbolically that the Devil is bound. What possibly could bind Satan that his power could not be used? The gospel of Jesus Christ. Romans 1:16 says the gospel is God's power to save. Satan can not defeat a person who obeys the gospel.
We must understand the 1,000 years to be symbolic as well. Numbers mean something in this book, if 10 means a complete number then 10 to the 3rd power indicates a very long period of time.
Verse 6 gives us a clue as to what the number 1,000 might be as well.
Rev 20:6 Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.
The period of time Christ is to reign is 1,000 years as well. If we can find out when Christ will reign we can find out about the number 1,000.
Eph 1:19 And what is the exceeding greatness of his power to us-ward who believe, according to the working of his mighty power,
Eph 1:20 Which he wrought in Christ, when he raised him from the dead, and set him at his own right hand in the heavenly places,
Eph 1:21 Far above all principality, and power, and might, and dominion, and every name that is named, not only in this world, but also in that which is to come:
Eph 1:22 And hath put all things under his feet, and gave him to be the head over all things to the church,
God gave Jesus power and authority over all things after his resurrection. He is seated at the right hand of God ruling and reigning on his throne right now. How long will he reign?
1 Cor 15:25 For he must reign, till he hath put all enemies under his feet.
So there you have it, the Devil is bound by the gospel during the time that Jesus reigns over the church. Does that mean Satan has no power at all? No, we know he does have power but he cannot overcome unless a person chooses to allow Satan into their life.
I hope this helps