What does "shift keying" mean in the context of digital modulation?
It's not (phase) (shift keying), for example. It's (phase shift) (keying). 

Another answer has explained why the word keying is used --- it dates to the days when modulation was controlled by a human operator using a telegraph key.

The phase shift (or amplitude shift or whatever) is because something is changing (shifting) when keyed.

If the system were manually operated, you could say that each time the operator pressed the key, the phase is shifted.