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) 
Here we begin to get more information about the nature of the problem in the Galatian churches. Paul had been to Galatia and preached the gospel to them. He notes with much astonishment that they have quickly fallen away from God to a different 'gospel' at the influence of false teachers, who we will call 'the Teachers' for the rest of our series on Galatians. Paul begins this way to lay out what was at stake.
The Teachers had been teaching something that was in opposition to what Paul had preached (we will explore more about the content of their teaching in a later post) and taught when he first came to Galatia. Paul construes turning from his gospel to be deserting God himself, which is why he was so concerned. One thing to notice is that 'turning' is a present tense verb (continuous aspect) which means that the action of turning hasn't been completed yet (Dunn p. 40). Paul is holding out hope that he can stop them from completely deserting God by abandoning the gospel.
Paul's rhetoric in verses 8 and 9 seems a bit harsh. It is helpful to note that overblown language was a typical element of Greek rhetoric (McKnight p. 59-60) and hence we don't have to feel compelled to call down damnation on those whom we believe are distorting the gospel. At the same time we don't want to minimize the fact that these verses show that Paul believed that the issue here in Galatia was of the utmost seriousness. The stakes are very high and certainly leading people away from God is the most serious crime one can commit. He wanted to stress the importance of getting the gospel right and try to begin a disassociation of the Galatians from the Teachers.
In verse 10, Paul is answering an objection laid against him. His goal, no matter what the Teachers claimed, was to please God in the way he preached. He did not claim that you received entry into the family of God by grace alone through faith apart from the Law in order to make it seem easy and gain converts.
 In my opinion the most difficult decision in outlining the subsections of Galatians as whether or not to include verse 10 with 6-9 or 11-12. I include it in this section because I think that the γὰρ (untranslated by TNIV usually translated 'for') in verse 10 is not completely concessive and hence verse 10 should be taken with 6-9 (Dunn p. 48).