Latch and flip flop circuits are used to store digital information. A latch can store a bit as long as power is applied, while a flip flop uses feedback to store a bit even after inputs change. There are different types of flip flops like SR, JK, D and T flip flops that store bits based on their input conditions and clock signal. Flip flops are edge triggered which means they change state only on rising or falling edge of the clock signal. This provides synchronization between logic and memory in digital circuits.