There's probably better ways to explain this, but here's my try:
The whole verse is:
that the creation itself also will be set free from its slavery to corruption into the freedom of the glory of the children of God. (Romans 8:21, 1995NASB)
This is an English translation that is almost word-for-word from the Greek. "Of" is showing (grammatic) possession, so we can rewrite the last phrase to see if it is easier to understand:
into God's children's glory's freedom
God's children is us.
God's children's glory can be a reference to many things, but they all boil down to us being in Christ and Christ being in us.
E.g.:
To them God has chosen to make known among the Gentiles the glorious riches of this mystery, which is Christ in you, the hope of glory. (Colossians 1:27, 1984 NIV)
The
freedom is most easily understood, I think, by noting that Paul is contrasting it with "slavery to corruption." This would be a reference to sin-taintedness which enslaves (John 8:34).
So, God's children's glory's freedom is the freedom we receive from being born again in Christ by which we are no longer forced to be slaves to sin. We are set free by Jesus.
The verse in question (Romans 8:21) refers to the sin-tainted creation will be freed in the same way that people are freed by being reborn in Christ. i.e., No longer slaves to sin; instead, pure and untainted by sin. This seems to also imply being free to worship God (ala Isaiah 55:12) with purity. If the creation will be subject to what people are subject to, then the universe must "die," then God will give it a rebirth, then the new creation will be pure and free from the taint of sin.
“Behold, I will create new heavens and a new earth. The former things will not be remembered, nor will they come to mind. (Isaiah 65:17, 1984 NIV)
Then I saw a great white throne and him who was seated on it. Earth and sky fled from his presence, and there was no place for them. (Revelation 20:11, 1984 NIV)
Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and there was no longer any sea. (Revelation 21:1, 1984 NIV)
The following verse parallels some of the same concepts:
For we know that our old self was crucified with him so that the body of sin might be done away with, that we should no longer be slaves to sin—because anyone who has died has been freed from sin. (Romans 6:6-7, 1984 NIV)
