A day is an in-game unit of time that lasts 24 (game) hours. For modules that use the standard game hour, this translates into 48 minutes (turns), which equals 480 rounds.
Things with a number of uses per "day" do not follow this time limit, though. Rather, such uses are replenished upon resting. So if an ability is "usable once per day," it can be used immediately after resting, even if it was already used immediately before resting. Furthermore, an ability that is "usable once per day" cannot be used a second time if the character with the ability has not rested, even if 48 minutes had passed since using it.