Sorry, perhaps I misunderstood your initial question the first time around.
Galatians 3:13 (KJV)
Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
The curse of the law, we know, is death (Rom 6:23). Christ redeemed his people by taking upon himself their sins and thereby taking upon himself the punishment that the law requires for sin. That punishment is death.
So when we read that we were buried with him, this wouldn't mean that we actually paid for sins with Christ, but actually means that when Christ died and bore the sins of His elect, that each elect identified with Christ's death because it was our very own sin that he bore. As such, we were redeemed.
But the application of our redemption takes place at different times. First the soul was raised to life (regeneration), while we still posses a cursed body of flesh that lusts after sin. Then in the last day, Christ's redemption will be applied to our bodies, when we put off this Cursed mortal body and put on our new incorruptible and immortal body.
1 Corinthians 15:53-54 (KJV)
For this corruptible must put on incorruption, and this mortal must put on immortality. 54 So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.
So, to answer your question, "What was quickened together with Christ?" It wasn't our flesh nor the sinful nature of our flesh. We know this because a true believer still lives in a body that lusts after sin.
Romans 7:16-18 (KJV)
If then I do that which I would not, I consent unto the law that it is good. 17 Now then it is no more I that do it, but sin that dwelleth in me. 18 For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not.
John 6:63 (KJV)
It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life.
There physical evidence of sin in our flesh (even if we're saved) is that we still die, as per God's law.
So, being "risen" or "quickened" together with Christ means that Christ's resurrection made eternal life possible for each person that he died for, because he paid for everyone of their sins so they they could never again die. This is eternal Life.
Colossians 2:11-13 (KJV)
In whom also YE are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: 12 Buried with him in baptism, wherein also YE are risen with him through the faith of the operation of God, who hath raised him from the dead. 13 And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;
Galatians 3:13 (KJV)
Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
The curse of the law, we know, is death (Rom 6:23). Christ redeemed his people by taking upon himself their sins and thereby taking upon himself the punishment that the law requires for sin. That punishment is death.
So when we read that we were buried with him, this wouldn't mean that we actually paid for sins with Christ, but actually means that when Christ died and bore the sins of His elect, that each elect identified with Christ's death because it was our very own sin that he bore. As such, we were redeemed.
But the application of our redemption takes place at different times. First the soul was raised to life (regeneration), while we still posses a cursed body of flesh that lusts after sin. Then in the last day, Christ's redemption will be applied to our bodies, when we put off this Cursed mortal body and put on our new incorruptible and immortal body.
1 Corinthians 15:53-54 (KJV)
For this corruptible must put on incorruption, and this mortal must put on immortality. 54 So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.
So, to answer your question, "What was quickened together with Christ?" It wasn't our flesh nor the sinful nature of our flesh. We know this because a true believer still lives in a body that lusts after sin.
Romans 7:16-18 (KJV)
If then I do that which I would not, I consent unto the law that it is good. 17 Now then it is no more I that do it, but sin that dwelleth in me. 18 For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not.
John 6:63 (KJV)
It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life.
There physical evidence of sin in our flesh (even if we're saved) is that we still die, as per God's law.
So, being "risen" or "quickened" together with Christ means that Christ's resurrection made eternal life possible for each person that he died for, because he paid for everyone of their sins so they they could never again die. This is eternal Life.
Colossians 2:11-13 (KJV)
In whom also YE are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: 12 Buried with him in baptism, wherein also YE are risen with him through the faith of the operation of God, who hath raised him from the dead. 13 And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;
When you get this figured out, the entire Bible will open up like never before.