A basic flip-flop circuit is a digital circuit that has two stable states and is used to store binary information. It operates based on the inputs it receives and the clock signal. When the clock signal triggers, the flip-flop circuit will either change its state (flip) or remain in the same state (flop) based on the inputs. There are different types of flip-flop circuits, such as SR flip-flop, D flip-flop, JK flip-flop, and T flip-flop, each with its unique characteristics and applications.