Why did Kate bow her head when William saluted on the way back to the palace? Honoring someone or something?

Probably as a form of curtsey. A curtsey is a traditional gesture of greeting, in which a girl or woman bends her knees while bowing her head.

It was a beautiful wedding. I actually looked this up online shortly after because I was curious too. If you notice he salutes and simultaneously she bows her head. She does this as a way to say a silent prayer for their dead soldiers. So they're each saluting but in a different manner :)