Localization: Sora in Kingdom Hearts (later Hallow Bastion visit)

So, bowing in the Japanese Culture has a lot of meaning.  The angle, how long you do it, the rank of the person, it all denotes different things.

Actually, Sony got into trouble after the PSN Hacking scandal because they did not bow for a full minute. ((And I can't find that now.  Here, have some info on bowing: it's a good primer))

Okay, now that that is out of the way... this should give you some idea on Sora's bow.

While English has "Grovel like a dog" or somewhat similar in our vocabulary, it does not do justice to this scene.  Due to the length and the position of him being on his hands and knees, Sora is putting himself so below Saix  he has effectively declared Saix to be his master.  He has (Possibly figuratively) Given up his freedom to be with Kairi. 

That has no English connotation.