'Out' can mean different things, but the general idea is 'completely'.
Sometimes that doesn't really make much difference, and the 'out' is used because it sounds better. e.g. Can you help me? Can you help me out? are very similar.
But there is a huge difference between "I'm bleeding" and "I'm bleeding out". "I'm bleeding" could mean "I have a paper cut". "I'm bleeding out" means I am losing a lot of blood. I'm losing so much blood that I am likely to die unless the bleeding is stopped. I am likely to run out of blood.
"out" can also refer to directions. "I'm going out" means I am leaving the building, or room.