The Equal Ground
Paul at no time thought of himself as being superior to anyone else; neither did he consider others to be superior to him. The only exception is on the occasion that he expresses his energy in exercising the Jews' religion -- Phil. 3:4 Though I might also have confidence in the flesh. If any other man thinketh that he hath whereof he might trust in the flesh, I more:
In the flesh he was more adept, more scholarly, more energetic, and more intentioned than anyone else in his religion; but in the Gospel Paul did not rely on the flesh but on God alone. Even the Apostles were off limits to his investigation. He trusted only God, for it was God who called him. No one intimidated him, nor were they seemingly intimidated by him. They all stood on equal ground before God: they owed it all to God and not man. Those who seemed to be "somewhat" were nothing to Paul (verse 6).
The Effectual Work
The Apostles "saw," or understood and were persuaded, that the Gospel of the uncircumcision (Gentiles) was committed to Paul, and they also "saw," or understood, that the Gospel to the circumcision was committed to Peter. Both Peter and Paul were persuaded (and so were the other Apostles) that the Holy Spirit (rendered by "he" in verse 8) had brought about effectually in both of them their calling to the Jews and the Gentiles respectively.
The Earnest Consent
Then a final decision was made for Peter that he and his followers were to evangelize the circumcision (Jews), and Paul and his company were to evangelize the uncircumcision (Gentiles). Thus the missionary direction was laid down for all time thence forward. Our evangelism is in tact; our plan is clear: we must evangelize the whole world (both Jew and Gentile) for the glory of God. Paul and Barnabas were given the right hand of fellowship for the approval to do this work of God planted in their hearts by the Holy Spirit.