[in a word, love].
Verses 3-4: Each person should examine himself so that he isn't fooled into thinking he is too important to help another. A Christian should not boast about doing good, or think he is better than another Christian.
Verse 5: A Christian should take care of his own faults and weaknesses, keeping humble.
Verses 7-8: Be assured that God knows all, and He will not accept mere words and professions of being a Christian if one's behavior is not as Christ would do. A Christian should be spiritual, not fleshly, because there are corresponding consequences to each way of living. When one lives to lower, base motives and fleshly ways, there is a corresponding degrading of one's character. If one lives in a spiritual manner, following Christ in a self-sacrificing way, his character becomes more like Christ, and life eternal is the result.
Verses 9-10: Following the law of love in helping others, especially believers, is the path to choose, and Paul cautions Christians to not become weary in this path of doing good to others.
Verse 11: Paul refers to his large handwriting, possibly caused by poor eyesight.
Verses, 12, 13, and 15: Summarizing the theme of the five preceding chapters, Paul tells the (Gentile) Christians in Galatia that they do not need to be circumcised according to the Jewish law. Circumcision of the heart only is the only circumcision required of the Christian, for whom old things have passed away. The Christian is a NEW creature.
Verse 14: Paul glories only in Christ, the Savior of the world. He rejoices in Christ; Christ brings him joy. The world is dead ("crucified") to Paul and he is dead to the world. Paul is dead to self-will.
Verse 17: Paul defends his apostleship, which some questioned. He physically bore the "marks of the Lord Jesus" from the blows and beatings he received because he was a Christian.
Verses 16, 18: Christians who live according to the rule of verse 15, as NEW creatures, are the "Israel of God." Paul seeks peace, mercy, and grace for them.
When we read this chapter, we are touched by Paul's humility, zeal, courage, total dedication to the Lord, to the Lord's word, and to his fellow Christians. We are encouraged to try even harder to follow these admonitions in Galatians 6 – to follow the law of love.