Promptness is a quality of arriving quickly or exactly when you're supposed to. German trains, which tend to pull into the station at the exact scheduled time, are famous for their promptness.
When someone compliments your promptness, they're either admiring your tendency to act immediately or your punctuality. If someone calls an ambulance for a medical emergency, its promptness is vital — someone's life could be on the line, so quick action is important. And when you have to catch an airplane, your taxi's promptness matters too. If you asked for a ride at 12:30 and your driver pulls up at precisely 12:30, you should thank her for her promptness (or just leave a nice tip).