A word hopefully most of you are familiar with, if not this is the place to look.
To expedite is to make things quicker, for example;
You’re at TFFR in the caribean and are told by ATC “XXX back taxi runway 12 line up and wait please expedite” the please expedite means DO IT FAST not slow! While back taxiing you should be on the runway so going over 35 knots won’t be a problem. This does not mean go full throttle up to 70 knots, I usually expedite a back taxi at about 40 knots ground speed.
This works the same with “exit runway when able please expedite” it means taxi off the runway ASAP so either inbound traffic can land on a clear runway, or departing traffic can get away.
I hope this helped!
If you have any questions feel free to ask, remember to expedite is to go fast!