This phrase, “supported voice” or “supported tone/sound” is used a lot in singing. It typically refers to a sound that is full and solid, has some “oomph” or carrying power and is not unpleasant. It’s not breathy, incipid, nearly inaudible, or monotonous.
auditorium/theater on your own lung power, you find out how hard it is to be heard without your trusty sound system. You realize that getting the voice to produce carrying power, or what used to be called in the old days, “projection” isn’t just a question of being loud. Loudness might be a factor, but if all you do is sing loudly, you discover in rather short order that it doesn’t hold up. Loud may not be the same as strong.