Having the second flip flop negative edge triggered ensures that the first FF holds its value long enough to satisfy the hold time for the second flip flop (since the clock trigger arrives half a cycle later). In the circuit the text refers to, the and-gates are enabled at the same time the flip-flop is toggled.

Why is edge triggering preferred over level triggering?

Edge triggering is a trick to allow devices to create a very fine level trigger which is faster than all external feedback loops, allowing devices to accept inputs quickly, and then close off the entrance in time before their changing outputs will change the values of the inputs.

What is negative edge triggering?

negative-edge-triggered (not comparable) (electronics) Describing a circuit or component that changes its state only when an input signal becomes low.