Why do the departure and arrival times on a scheduled airline differ from the information on the airline's web site?
Airlines generally display the times that the aircraft departs and arrives from a gate. FlightAware presents the time that the aircraft departed and arrived, also known as the "wheels up" and "wheels down" times. At large airports or in various circumstances, there can be a significant difference in these times due to delays on the ground.

Why do I care about wheels up / wheels down time for airline flights? Shouldn't I just track an airline flight on their web site?
Maybe so; that's a good point. FlightAware's data may or may not be the most relevant for airline customers depending on the situation. One interesting aspect of FlightAware's tracking data for airlines is that although it doesn't offer gate arrival or departure times, if an airline is claiming (for example) that flight #482 will arrive at gate E6 at IAH at 4:18pm but FlightAware says the flight isn't going to touch down at IAH until 4:32pm, you might expect a delayed arrival at the gate or, less likely, a revised ETA from FlightAware.