I was taught it refers to what pitch is played in response to a written C on the page. That is, a euphonium in C plays (no matter the clef) a concert C when seeing a written C;a tuba in E flat plays an E flat when reading a written C, and so on. That understanding works when, for example, when I've seen some European bass clef parts notated euphonium in B flat and the euphonium is expected to play a B flat when the written note in bass clef is C.