some plants have crisp stems and are more easily pinched than trying to use pruners which actually cause the stems to split and shatter. This in turn can cause the plants to partially die which is not what we want to happen. Pinching tends to lose the wound without causing the stem to shatter or crack.
People pinch to make the plants which are loved for there foliage to become fuller. ie daylillies and salvia.
Another reason is to get rid of old flowerheads which makes the plant produce more flowers.
The last reason to pinch flowerbuds off is to get the plant to flower later in the season when other plants are dying out instead of in the midst of summer. ie mums and asters.