Usually referred to as a rope.
Your rope is tied to a harness that goes around your waist and thighs. It is then looped through some kind of protection on the wall, (a bolt or gear or anchor...
It is an assortment of quick draws, hexes, camming devices, nuts, carabiners, and anything else you may need for a particular climb. The rack is usually attached to you by your harness or a sling...
There are several types of equipment in rock climbing such as the harness, rock, climbing shoes, belay devices such as ATCs and GriGris, Chalk (optional), and helmets.