What does Genesis 24:34 mean?

Abraham's servant is convinced that God has chosen Rebekah to be Isaac's wife. Now sitting before her father and brother, the servant will tell the story of how he came to them and make his case for why they should accept this offer of marriage on her behalf.

He begins by revealing who he and his master are. He doesn't name himself—despite assumptions that this man is Eliezer (Genesis 15:2), he is never identified in this particular story. In fact, the servant never sees himself as central to the story, at all. This is not even about him. He represents Abraham. For the first time, he reveals to them that their relative Abraham, Nahor's own brother, is his master and the reason he is before them now.