If you're looking for the technical definition these guys are right
If you're lookin for a ghetto definition - Profile means the distance from the edge of the tire (say where the tire touches the ground) to the edge of the RIM. Low profile means that this distance is less than the normal 50-65 width.
So 40 would be low profile.
*guys don't flame me .. i'm not that ghetto - i could be wrong about this!!!