What does Genesis 33:3 mean?

Jacob ran away from Esau years ago to avoid his vengeful wrath (Genesis 27:41–45). He has already split his caravan in case of violence (Genesis 32:7–8). He has sent lavish gifts ahead to Esau (Genesis 32:13–15). Jacob has even arranged his immediate family in what seems to be an order of preference, with his most treasured wife and son at the rear (Genesis 33:1–2). As this verse shows, Jacob intends to approach Esau first, which might explain the formation in which he organized his loved ones. If Esau attacks, it will be Jacob who is killed first, and the rest might have a chance to flee.

At long last, Jacob presents himself to his brother, going before his carefully arranged wives and children. He interrupts his forward progress seven times to bow low, all the way to the ground, before Esau. In ancient times, a servant may have bowed seven times to show respect to his lord. Jacob has done all he can to repeatedly make clear to Esau that he sees himself as the servant and Esau as the lord.

In point of fact, Jacob holds both birthright and blessing (Genesis 25:29–34; 27:28–29). He may feel he holds these illegitimately and wishes to show Esau that he will honor him as the superior, instead. Or, he might simply be expressing apology and humility to someone he's wronged.