Most plaster walls and ceilings built before 1940 were constructed using wood lath as the substrate for the base coat of plaster. The thin strips of wood allowed a sturdy foundation through which the rough base coat oozed and gripped the back of the lath. These "keys" held the heavy plaster structure firmly in place.
Behind the wooden lath on your ceiling you'll probably find electrical wiring for ceiling fixtures, as well as the supports for the fixtures themselves. If the room is directly below a roof or attic, there is likely to be insulation between the lath and the attic floor boards. You might also find duct work for heating and air conditioning and plumbing vents. If the ceiling is under another living space, there probably isn't any insulation, but you'll still find wiring and perhaps heating and air conditioning ducts.
If you've removed the plaster from the ceiling and are left with wood lath, you can probably see that there is a lot of debris above it. In fact, you probably already know that if you tap on the lath, a lot of grit and dust will fall through it. While a lot of debris will fall through the lath, larger, broken pieces of the keys that held the plaster in place will not. You should also be prepared to encounter rodent droppings, dust from the same and perhaps the critters -- dead or alive -- themselves.
When removing plaster, always use a dust mask or respirator and safety goggles to protect your lungs and eyes. If there is any reason to suspect that your plaster contains lead paint or asbestos, you'll need to consult an abatement specialist to confirm their presence and give guidance on proper removal. Applying a new plaster ceiling to intact wooden lath is possible, but plasterers skilled in such old-fashioned techniques are scarce and come at a high price.