A wadcutter is so-called because of the clean holes it makes in a target. A target shot with these bullets resembles what's left of a piece of material cut into shotgun wads with a sharpened pipe, termed a "Wad Cutter."
Wadcutters were developed to make those sharp, clean holes, because in most shooting events the rule is "a shot that cuts or touches a scoring line counts for the higher value." Shoot a .22 round nose at a sheet of paper and note how difficult it is to find the edge of the hole for scoring purposes.
Back in the 1840s, Whitworth demonstrated that a flat nose steel projectile penetrates steel armor best -- a sharp nose is likely to be deformed on impact. For that reason, most armor piercing tank and naval projectiles have a flat nose under a ballistic windshield.
A lead wadcutter is not an armor piercing bullet, by any means. In hunting, however, wadcutters and semi-wadcutters tend to cut full-diameter holes in game, and kill quite well.