The logical equivalent to "and". Saying so to folks who haven't had any courses in logic or programming or higher mathematics produces blanks stares.
It is in our use of informal language that "but" takes on confusing contextual connotations (see: alliteration); there is no logical difference between the phrase "I'm young and brilliant" and "I'm young but brilliant," but in language we assume that in the latter case the two adjectives must be contradictory.