"But if Christ is in you, although the body is dead because of sin, the Spirit is life because of righteousness." (ESV)
1st: What is "the body"? It is the same as "the flesh" in v. 11. The body is you, your actual physical being.
2nd: Why is the body dead? Sin (begun with Adam) brings death physically. This is actually a great grace of God that he didn't allow Adam and Eve to live in their physical bodies forever. To live in a fallen, sinful body forever would be terrible and utter misery.
3rd: All physical bodies will die because of sin. (Spiritual death also comes from sin, but we will set that thought aside for now.)
4th: The Spirit - speaking of the Holy Spirit - is life because of righteousness. What does it mean for the Spirit to actually be life? Look to verse 11. The Holy Spirit of God, who is God, is the person who raised Christ from the dead and the Spirit's presence in a person is a guarantee that their physical bodies will be raised, resurrected from the dead. The Holy Spirit is the only thing that "is life" for the Christian, because he will give them eternal life in a final, fully redeemed, completed manner when he raises from the dead those who he dwells in right now.
5th: Whose "righteousness" is referred to in this verse? This foreign righteousness is the cause of the Spirit to give and be life to the one in who the Spirit dwells. So whose is it? Allow me a summary statement of the Bible, but righteousness that is given to man always finds its source in the Son of God, Jesus Christ. (See Romans 3:21-26 for a brief support of this idea.)
6th: Something that may be confusing is the fact that Paul speaks in the present tense even as he refers to resurrection life from the dead. "The body is dead" and "the Spirit is life". Don't ask me about the Greek, because I don't know it and I don't want to pretend like I do.
What Paul seems to be getting at here is that the body, right now, is as good as dead. What is guaranteed in life? Death (and taxes, as the saying goes). Everyone who reads this post will physically die. (I'm not going to speculate on Christ' return and all that jazz here as so many feel the need to comment about. :-P ) Likewise, and I think this is where the Christian really can draw all of their hope from, Paul is saying that your new, eternal, glorified life, is basically in effect right now in the manner of speaking that this resurrection is 100% promised by God. On a similar note, and for your meditation, does not Romans 8:30 say that we are - present tense - glorified according to God's promise? Food for thought.
I think that is all I have for now on this. I hope it was helpful even though much of it was simply explanatory and I didn't seek to draw a ton of applicative points out of it...although I think we can find great joy, hope, exuberance in what I talked about in the 6th point.
Oh, and this post was spurred on by a request from a fellow friend on Twitter! Looks like the internet is good for something after all. :-)