Is "departure time" when the plane leaves the gate or when it takes off?
Seems like every single flight I take is delayed, but I can't tell how badly. If I have a flight that has a "departure time" of 5:20 PM, for example, and it leaves the gate at 6:30 and takes off at 6:50, is that a 1 hour and 10 minute delay or a 1 hour and 30 minute delay?
In general, the departure and arrival time are considered the time that the parking brake on the plane is released and applied respectively. For most major airlines, this is actually recorded automatically - the moment the brake is released the 'departure' time is recorded, and the moment it is re-applied at the destination the 'arrival' time is recorded.
On departure the parking brake is only released once the entire plane is boarded, the jetbridge/stairs have been removed, and the plane is ready to actually start taxiing (although in practice it might not actually taxi at that time due to any number of factors including other planes blocking it).
On arrival, the parking brake is set only after the plane has arrived at the gate, and before the seat-belt sign is extinguished and the jetbridge/stairs are bought to the plane, and before the door is opened.
In some cases a slightly different definition is used. For example the European Union "EU261" compensation uses the time that the aircraft door is opened as the arrival time.
So in the example given, the flight is at most 1 hour and 10 minutes delayed - although it could be less if the plane was ready to taxi before it actually started doing so.
In general, the exact length of a delay on departure is not all that relevant. What is generally seen as far more important is the arrival delay, which will frequently be significantly less than the departure delay.
There are a few times (depending on who is measuring it):
The block time (airlines measure this) - this starts and ends when the plane starts and stops moving. The flight dispatcher (staff responsible for the flights departure) is the one that actually clears the plane to move. Once the parking brake is released by the cockpit, there are certain timers that start automatically in the to record the flight.
The departure slot - this is the time slot given to flight from the tower. There are many airlines given the same departure slot; and they must start moving within a certain time limit of this slot, otherwise they are pushed back into the scheduling queue.
The departure time - this is the time, after which, the airplane cannot be boarded. It is considered secured for takeoff. All ground people are removed, the doors are closed and armed. However as a passenger (unless you pay attention to the announcements) you may not know when this happens. Sometimes the flight senior will announce this, sometimes the pilot will announce this.
Now as far as passengers are concerned, you are really only worried about the departure time because all other times of concern are calculated based on this time.
Scheduling and on-time performance is one of the many factors that determine the cost for servicing a route. A delay is always avoided; however an early departure can also be problematic (you may not make a specific landing slot on time, or your arrival gate may not be available to you causing you to park on the apron or a longer taxi, etc. etc.)
Departure Time is when the flight is scheduled to leave the gate. Most importantly (to you), it's when the gate is closed and (normally) passengers may no longer board. You might sit at the gate for a while before you're cleared for pushback, depending on traffic (and other factors).
In your example (flight is scheduled for 05:20, actual pushback at 06:30, takeoff at 06:50), that flight would be delayed by 1h 10m. Note that it might be moved up in the queue for takeoff, so the delayed arrival time might be less than 1h 10m. But there are many variables.
Not directly an answer to your question, but when you speak about flight delays, the departure time is not what actually matters. What matters is the arrival time. And at least in the EU, that has a definite, legal answer: The plane counts as arrived when the doors open.
I see some answers and comments here that get this part wrong, which I why I'm posting this answer. Maybe the US is different, though.
Source: https://www.bottonline.co.uk/flight-delay-compensation/claim-guides/definition-of-arrival-time
1:10, but that's not the end of the tale. Airplanes can make up time and post an improved arrival time... but not so likely in your case. Regardless, it's not over til it's over.
I have seen airlines intentionally pad the schedule: an uneventful on-time departure usually results in an early arrival IME, and even a slightly late departure can result in an on-time arrival. That is one advantage of air flights, which are scheduled by segment; trains can't pad except at the final destination - and they can't leave a station earlier than carded.
A late departure may be for connecting passengers whose plane is itself late, and for whom the alternative would be an overnight stay, ruined plans, and great expense and trouble for the airline too.
Now if you want to know more about the flight aspects of this, you could re-ask this question over on aviation stack exchange.
