6 I am astonished that you are so quickly deserting the one who called you by the grace of Christ and are turning to a different gospel— 7 which is really no gospel at all. Evidently some people are throwing you into confusion and are trying to pervert the gospel of Christ. 8 But even if we or an angel from heaven should preach a gospel other than the one we preached to you, let that person be under God's curse! 9 As we have already said, so now I say again: If anybody is preaching to you a gospel other than what you accepted, let that person be under God's curse!
10 Am I now trying to win human approval, or God's approval? Or am I trying to please people? If I were still trying to please people, I would not be a servant of Christ. (TNIV)
Right off the bat it seems pretty clear that Paul had opponents in Galatia. Who were they and what did they teach? In his Galatians commentary, J. Louis Martyn provides a detailed answer that is very helpful on pp. 117-126. I'll sketch his answer very briefly below (and try to avoid the debate over the New Perspective on Paul, for now) because it's critical that we have a general understanding of what Paul was arguing against in order for us to understand what he was arguing for.
The Teachers were Jewish Christians with ties to an influential portion of the Jerusalem church whom they believe they represent. They were not present in the church at Galatia when Paul founded it, but later came to Galatia, perhaps seeking their own Gentile mission. Like Paul, the Teachers probably called their message 'the gospel,' creating confusion, since their gospel had the Law as the point of departure rather than Christ. Rather than through Christ alone, it was through the Law that one became part of the people of God and thus received God's Spirit, and to follow the Law correctly one needed to be circumcised. Jesus was secondary to the Law.