A flip-flop is a one bit memory cell. When the CLOCK input receives a rising edge (a 0V to 1V transition), it will capture the current digital state of the input. It will hold the captured value on its output until another clock edge is received, at which point it will sample the input again. Many flip-flops also have a RESET input allowing you to clear the stored value so that the output becomes low again.
By the “digital state” of the input signal, I mean that its only possible output values are “high” corresponding to a “high” input (in LZX land, a high output will be 1V. an input will be high if it is at least 0.5V.) or “low” (0V, or less than 0.5V) – the actual analog value of the input signal is only compared to see if it is at least “halfway on”. A flip-flop is sort of like a sample-and-hold except that it will only output 0V or 1V, not any analog values in between.
Example usage of the Castle flip flop in a patch:
Castle Patching 002: Digital Sample and Hold
You may be able to find more examples by searching this forum for flip-flop.
More details about implementation and applications: Flip-flop (electronics) - Wikipedia