I don't think SS uniform skull is in any way related to similar insignia in other nations, as suggested by @TheHonRose. I believe it was introduced by Hugo Boss circa 1933 when he designed Nazi uniforms, and the meaning of it was something like "Loyal until death". I don't recall the reference though; you may want to look into early history of Hugo Boss fashion house.

Now, as to where Hugo Boss got the idea of putting a skull on SS uniforms - that I don't know; Oldcat's conjecture about Totenkopf sounds very plausible.

Wrong. hugo boss did not design any german uniform used in ww2. They where designed by Karl Diebitsch and Walter Heck, none of them worked for Hugo boss. Neither did hugo boss design any skull for the uniform..hugo boss like so many other simply made the stuff that was ordered.