A repetition has the function of setting a brief, high tension in every angle. You can think of it like make the fibers 'play' one after another while contracting your muscle. The second limitation of 'full range of motion' is for danger of injuries, because there are many exercises where its rather dangerous to fully stretch a muscle under load. The slower you contract a muscle, the more tension can be developed in that there are more contractile units in the muscle that get connected. You train with more weight than you actually could and should.
Many injuries come from explosive lifts.
I'm very glad that the knowledge of slow training is spreading across gyms and among bodybuilders these days. The intramuscular friction brakes the movement while lowering a weight. Thats the reason why you can lower pretty much more weight than you can lift. In doing the negative phase of a repetition very slowly you try to emphasize the tension during this phase. You will perhaps not believe me, but I trained for ten years in heavy duty style without warming up a single time and never get hurt.