6 So also Abraham “believed God, and it was credited to him as righteousness.”
7 Understand, then, that those who have faith are children of Abraham. 8 Scripture foresaw that God would justify the Gentiles by faith, and announced the gospel in advance to Abraham: “All nations will be blessed through you.” 9 So those who rely on faith are blessed along with Abraham, the man of faith.
10 For all who rely on the works of the law are under a curse, as it is written: “Cursed is everyone who does not continue to do everything written in the Book of the Law.” 11 Clearly no one who relies on the law is justified before God, because “the righteous will live by faith.” 12 The law is not based on faith; on the contrary, it says, “The person who does these things will live by them.” 13 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 pole.” 14 He redeemed us in order that the blessing given to Abraham might come to the Gentiles through Christ Jesus, so that by faith we might receive the promise of the Spirit. (NIV)
In this section Paul continues his argument that Gentiles are part of the people of God by faith. In the prior section Paul argued from experience. Scripture is the basis of his argument here. Abraham is used as an example of one who was considered righteous on the basis of his faith. However, we need to see that Abraham is more than an example, he's the archetype. Paul selects Abraham because he is the father of the family, the patriarch of the people of God. What's true in his case is normative for his descendants. We can be a bit more specific regarding Paul's argument than that, though. The clearest summary of verses 6-9 comes from Dunn and I will replicate it below:
Abraham's righteousness-->faith-->Abraham's children (iii.6-7)
Abraham's blessing-->faith-->all the nations (iii.8-9) (p. 168)
What Paul's doing in verses 6-9 is showing that Abraham's children contain members of all the nations by arguing that the basis of righteousness and blessing isn't circumcision, it's faith.