What does the esp button do on an Audi A4?

Despite what You've heard, the ESP button on Your AudiA4 has nothing to do with predicting the future. Instead, that's Your electronic stability progRam setting, which is a computerized technology that tries to improve Your car's stability by detecting and preventing a loss of traction. Usually, this is the sort of thing You want. There's a fun way to think of this button, and that is to be the "Engage Snow Play" switch. See, the way this works is it actually decreases engine power, so You don't "spin out". But, if You're stuck in the snow (because who doesn't like having a bit of fun) it prevents You from "digging" out with the wheels. Mud's another time You'd want to actually turn the ESP off. When You do, there'll be a little triangle with circles on the dash; don't be alarmed, and don't be afraid to disable this when the situation requires!