Sink clips come in three varieties. They are used in rimless sinks, under-mount sinks and counter-over sinks. The self-rimming sinks do not have clips and are sealed using caulk or plumber's tape. The three styles of clips secure the sink from under the counter to hold it in place. The type of clip used is based on type of countertop and the sink purchased.
The clips for a rimless sink are placed directly beneath the countertop. The clip is tightened to pull the counter and sink together. The clip uses pressure and gravity to hold the sink in place.
The under-mount sink uses a clip that is fastened under the counter. A T-slot is cut into the bottom of the countertop. A bolt is then slid into the slot and threw the clip. A wing-nut is used to tighten the counter to the sink clip.
The counter-over sink is placed directly on the base material of the counter. The countertop is put on top of the base material. The clip is attached under the base material and tightens into the sink. Gravity hold the clip into place.