When you hit a guy with a clean counter, you are using his momentum against him, and he is in no position to deflect, roll with or otherwise avoid the punch. And it is all counter punching, even your attacks, because they draw a response and you'll land your best shots as counters to those.
I think the highest level of boxing is when you are not merely reactively countering, waiting to see what he throws and then reacting to it. It is when you know what he is going to throw before he does, because you are making him throw that particular punch. Either by feinting, or by 'giving' him an opening to punch at. Watch this fight:

Lopez knew he was going to throw that right hand because he made him throw it.
Last, when you are practicing your slips and counters, don't get in a hurry to counter with a bunch of punches. Get the slip and that first punch down tight because that first one will likely be the most damaging blow; learn to get that one home and then build on it. Don't neglect the first one by getting in a rush to let your hands go. One well timed and well placed punch will accomplish more than a flurry that is off beat.