1. slang To decline or reject someone or something in an app. The phrase was popularized by the dating app Tinder, in which users "swipe left" on the screen to reject a potential mate. That girl is pretty—I'm only swiping left because I'm not into blondes. Ugh, this guy's has no sense of humor—swipe left! I keep swiping left because these dresses are all hideous.
2. slang By extension, to reject or decline something. Studying instead of a night out? Definitely swiping left on that.