A curse for us

"Christ redeemed us from the curse of the law by becoming a curse for us, for it is written: 'Cursed is everyone who is hung on a tree.'"

Galatians 3:13 is one of the Bible's clearest short statements of penal substitution, and thus of the authentic gospel (which it is Paul's purpose to defend, Galatians 1:6-9). (Penal substitution has been discussed here most recently here, here, here).

What is taught us in this verse?

1. We were exposed to the curse of the law: we were under it, and stood in need of redemption from it. (Note that Paul is writing to uncircumcised Gentile Christians here - this is not just Jews who were under it. This observation has implications for various other theological ideas floating around).
2. Christ is the one who has brought us out from under this curse. He redeemed us.
3. He did this by himself taking the curse upon himself. He hung on a tree: he was cursed.

That's penal substitution. Penal substitution means two ideas: there was a punishment due (a penalty), and that somebody else other than the offender suffered it (substitution).

Many theologians have toiled long and hard to make this an obscure, difficult or controversial question. Regrettably, some solidly evangelical men have also fallen into the trap set for them of talking of penal substitution as a "model", implying that it is a human reconstruction, one possibly viewpoint amongst many. But it is not a difficult one, nor one alternative on a menu. It is a simple statement of what Christ did, from which all the other benefits and achievements of Calvary flow out: it is the foundation that undergirds everything else that can be said. (e.g. Calvary is the great victory over the powers of evil, "Christus Victor", precisely because by a substitutionary atonement, Christ has robbed those powers of their hold over man - sin being forgiven, God no longer needs to punish man, or leave him to be a slave to his sinful nature; the possibility of new birth and a new life and new society is opened up, and hell is raided for its inhabitants, etc.).

According to Paul, this is the gospel, and no other alternatives are allowed; indeed, they are all damnable - Galatians 1:6-9. It's there in words of very few syllables.