Engine cooling fan comes on when car is not running?

Because, many cars now (and in the past) have electronic fans. (they used to be all belt driven, but not anymore). Just because the car is off, doesn't mean its really off. The car will still continue to cool itself off. If the coolant gets too hot inside the radiator, it can pop the pressure valve and will the shoot out into the overflow tank, or possibly onto the ground.

The fan turning on prevents this. :) Don't worry, its normal

... or, if the car is stone cold, and the key is switch on, and the fans run, then there's an incomplete circuit.