Hello Birdie,
The word 'angel' means messenger. In this case, the messenger who binds Satan is Christ. He is the one who came down to earth to go to the cross and be resurrected. (I saw an angel come down from heaven) This caused Satan to be bound in the following way: He could not deceive those who God now allows to believe on Christ unto salvation.
Let's look at the scripture:
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Then I saw an angel coming down from heaven with the key to the Abyss, holding in his hand a great chain. He seized the dragon, the ancient serpent who is the devil and Satan, and bound him for a thousand years. And he threw him into the Abyss, shut it, and sealed it over him, so that he could not deceive the nations until the thousand years were complete. After that, he must be released for a brief period of time.
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So first of all, just for proper exegesis, there is nothing in the context that would identified the angel as being Christ. It would be by conjecture only to interpret him as such.
Secondly, the Abyss is a literal place under the earth. It is the same place that that those demons collectively called "Legion" begged Jesus not to send them into, as revealed in Luke 8:30.
The Abyss is also the current location of the beast, that angel of the Abyss, as revealed in Rev.9:11, 17:8. The Abyss is a real location under the earth. Therefore, when it states that this angel throws Satan into the Abyss and locks and seals over him, then he will literally be putting Satan under the earth in the Abyss so that he has no contact with the inhabitants of the earth during Christ's thousand year reign.
It is necessary to compare and cross-reference scripture to come to a right interpretation. Satan's binding is not metaphorical, symbolic or spiritual, but is literal.
At the sounding of the 5th trumpet, anther angel has the key to the Abyss and will literally unlock it, allowing those demonic beings to come out to torment the inhabitants of the earth. From that time, the Abyss remains open until the Lord returns to end the age. Then in Rev.20 another angel having the key to the Abyss throws Satan in and locks it back up. This is a literal lock up so that Satan is cut off from influencing the inhabitants of the earth during Christ's thousand year reign, where it will be a time of peace on a paradise earth, where prey and predator animals and their young lie down together, with a young child leading them around. It will be a time when the lion will eat straw like the ox.