A redpoint is a successful lead climb of a route after the climber has previously attempted (and usually fallen on) it. The climber may have rehearsed the moves, worked the beta, and learned the rest positions during prior attempts — but on the redpoint go, they climb cleanly from the ground without falling or weighting the rope.
Redpointing is the dominant style for sport climbing at all levels above beginner. Almost every hard sport route is sent as a redpoint rather than first-try. The term comes from German climber Kurt Albert, who in the 1970s painted a red dot at the base of routes he had climbed cleanly without resting on gear — establishing the standard that distinguished free climbing from aid climbing.
A redpoint is contrasted with two cleaner styles: a flash (sent first try with prior beta) and an onsight (sent first try with no information at all). All three are valid sends, but onsight > flash > redpoint in climbing's informal hierarchy of style. Most climbers redpoint their hardest sends — sustained climbing at the limit usually requires multiple sessions of work.