It's not the honours specifically, it is the different ways of referring to somebody.
The Oxford English Dictionary says (s.v. "style",n, 18)
a. A legal, official, or honorific title; the proper name or recognized appellation of a person, family, trading firm, etc.; the ceremonial designation of a sovereign, including his various titles and the enumeration of his dominions.
This presumably developed from meaning 15. "A manner of discourse, or tone of speaking, adopted in addressing others or in ordinary conversation." or something like it.