Edge triggering, flip flops
It is neither 0 nor 1. An edge means a transition from 0 to 1 (positive-going edge) or from 1 to 0 (negative-going edge).

An edge-triggered flip-flop is a device which performs its task only when the clock input detects an edge. That is, only in the instant when the edge is detected the FF does its job.

Terminology note: usually you'll see shorthand terms like "positive edge" and "negative edge". They mean the same as "positive-going edge" (a.k.a. rising edge) and "negative-going edge" (a.k.a. falling edge).

To be more specific, since I explained the thing in a very simplified way, you should be aware that the other inputs of the FF must meet some timing requirements relative to the clock edge in order for the FF to behave correctly.

In particular, the inputs must be stable for a minimum time before the clock edge (that's called the setup time) and must remain stable for a minimum time after that edge (that's called the hold time, which can sometimes be zero, for specific technologies).

If you don't meet those requirements your FF (or any other synchronous sequential digital network, which is the category to which the edge-triggered FF belongs) may (and usually will) do funny things (read: it could misbehave).