Push-back, basically.

From memory, I think that the time that is communicated via ACARS is parking brake off. So if the aircraft is ready, the tug is connected, and the parking brake is off but the aircraft has to wait before actually pushing because of (eg) movements behind it, then the actual departure time may be recorded as slightly earlier than actual push-back.

Interestingly, ISTR from previous discussions that for the purposes of the ANO, a "flight" only begins when the aircraft begins to move under its own power. So presumably that would exclude push-back and engine start (and any tow to a remote engine start position), and the "flight" only commences when the aircraft taxies by itself. But that is of course for different purposes from "departure time".