A short introduction on the word level:
- fahren means 'to go by means of transports', 'to drive' or 'to ride' (whereas gehen is going by foot).
- abfahren (and abgehen, accordingly) literally means 'to go off'
- Abfahrt (resp. Abgang) is the corresponding noun, literally meaning 'the go-off' (= start, departure etc.)
That being said, Abfahrt belongs to a figurative semantic field with abgehen in its center that is used to express 'to go down' (note the similarity), 'all hell was let loose', 'to whoop it up', 'to paint the town red' etc. It's probably cognate to the idea of let's go in English:
- Jetzt geht's ab (also … geht die Post ab) means 'now it's happening', 'now it's going down'
- abgehen figuratively means 'to go wild'
- Abfaaaaaahrt! is a common fire-up slogan by carnival barkers on fairground rides. Maybe because of that, Abfahrt has been a joking expression for let's go in other contexts.
It's notable that as a verb, only abgehen is used in the figurative sense, the corresponding noun Abgang is not. Inversely, the noun Abfahrt is used figuratively (maybe originating in the fairground rides), but not its verb abfahren.
In the song, it is also used like on fairground rides to fire the listeners up for the forthcoming drop of the song (like a 'rave signal'). The best translation in this context is probably just let's go, but nevertheless Abfahrt conveys many more connations (concerning going wild) as stated above.