Bowing is used as a way of greeting, however how deep of a bow that's used has a lot of meaning.
And in this case Obama sent the signal that the Emperor is his superior whether he knows it or not and by extension that Japan is the superior to the U.S.
Anyway I think Obama was one confused puppy when he got that handshake instead of the bow he more than likely expected.
The Emperor looks as if he's saying "Heh, heh, heh."