What does Genesis 24:27 mean?

When Rebekah reveals that her grandfather is Abraham's brother Nahor, the servant recognizes that God has indeed answered his prayers and brought him right to the doorstep of Isaac's future wife. He stops in the middle of his conversation with Rebekah and worships the Lord.

His prayer reveals his heart. First, the servant blesses the Lord, addressing him once more as the God of his master. Next, he expresses his gratitude and relief that God still has steadfast love and faithfulness for his master. The servant was clearly concerned that if this mission failed, it would suggest that God was no longer concerned with Abraham.

Finally, the servant includes himself in the prayer, giving God the credit for leading him not only to some distant relation of Abraham's, but to Abraham's own immediate family relations.

One note: It was apparently common in this era and in Abraham's family for close relatives to marry each other. This early in human history, there was apparently little risk of genetic issues resulting from the offspring of family members, and God had not yet forbid Israel from marriages between close relatives. In fact, it will become clear that God very much intended for Isaac to marry his cousin Rebekah for the purpose of creating a people that were uniquely His own.