Though of course Webster1913 always does it so well, I'd like to add a little.
As we know, the Germans call themselves Deutsch, not Germans. Deutsch ultimately derives from the Old High German diot, which literally means "people"--the Deutsch are the People; it has the same origin as Teuton. This is similar to the Irish Tuath, a tribe or people, as seen in the name Tuatha de Dannans.
So why do we call them Germans? German comes from the Latin germ and nus, "of the same stock" that is, germen a bud or sprout. In other words, the Romans refered to "those northern tribes" as being of the same origin--Germani.