These new teachers insist that for Christians to be truly faithful, they need to follow Jewish law. Foremost, men need to accept the sign of the Jewish covenant and be circumcised. Paul believes that this is a complete misunderstanding of the gospel. Jesus is the new vehicle for the original covenant between God and Abraham. Through Jesus (and the power of the Holy Spirit), all people can become faithful to God. This requires faith in Jesus -- for Paul, a specific understanding of the purpose and meaning of Jesus' crucifixion and resurrection.
Again and again, Paul tries to make this clear to the Galatians, often in rather exasperated tones (and frequently with double entendres related to circumcision). Rather than trying to learn and follow the numerous regulations of Torah, Christians need to focus on two things only -- being heirs to the covenant through proper belief, and bearing the fruits of the Holy Spirit -- the signs and consequence of faithful behavior -- in their lives.