If you're using free weights, this means returning to your starting position after every rep: If you're doing bicep curls, lower you hands all the way down and bring them all the way back up. To get the most complete range of motion when using a weight machine, you should lower the weight so it almost touches (but doesn't quite touch) the weight stack below.
If you're not sure what the range of motion should be on a particular exercise, ask a trainer at your gym. But whatever you do, don't just go part of the way. If you find you can't complete a full rep, it probably means you should switch to a lighter weight.