Flip-flops are bistable multivibrators that can store binary data and change between two stable states (high and low) under the influence of a control signal. They can be classified into three types: latches, pulse-triggered, and edge-triggered flip-flops, with specific varieties including S-R, J-K, D, and T flip-flops, each having unique operational characteristics and uses. Flip-flops are crucial in digital circuits for data storage and control of functionality, serving as fundamental components in register devices.