It varies depending on the airline.
Usually for airlines/aircraft that use ACARS, the 'brakes released' time is used as the departure time (so regardless of whether or not it was held on stand for 10mins due to aircraft taxiing behind, it departed on time).
For the majority of other airlines who don't use ACARS, the departure time is when the wheels start to roll (or when engines are started if the APU is inop and an ASU is required).