It's a term to represent that they can deal high damage in second, like with real life gun they say 'rounds per minute'. Most guns don't have mags that could last one minute of continues fire but it's the estimated amount based off it's fire rate, because if constant nerfs and buff to different characters no one bothers using say 'hanzo is a 50 dps'. It's just said dsp to pretty much say high output of damage per second even if say hanzo or mcree who's fire rate might be slower then others their high damage per shot makes them fit into said role
it means damage per second, it came from earlier MMORPGs like WoW (idk what origanted) but stems from heroes like tracer that deal good damage over intervals of time, vs heroes like reaper which are burst damage
DPS is kind of misleading. It stands for damage per second, but it's often aimed at offensive heroes. DD (damage dealer) is also something you might hear, which basically means the same. Most offensive heroes have a high DPS, so that's probably where it started.
Yeah stands for damage per second which is sorta wrong
But i guess people dont know the meanig of dd or could think that people would pick hanzo or widow then (they do it anyways lol)