These are the class of sequential circuits which are governed by a global clock signal generated by an oscillator. The state of all elements of a synchronous circuit changes only by an application of a distributed clock signal. So, this makes the state of a synchronous circuit predictable. Also, synchronous clock signals are less susceptible to noise, circuit anomalies and hence safer to design and operate. But they are limited in operation of speed by the propagation delay of the clock signal in reaching all the elements of the clock signal. The time period of a clock signal should be long enough to accommodate longest propagation delay. Practically all the circuits today are synchronous circuits, except the part where speed of the circuit operation is crucial.
Asyncronous circuits change state only through the inputs received by them. So, the operation is quite instantaneous since they dont have to wait for a clock pulse. They are limited by propagation delay of logic gates only. But asynchronous circuits can transition into a wrong state due to incorrect arrival time of 2 inputs. This is called a race condition. Asynchronous circuits are quite difficult to design for a reliable operation. These are used primarily in high speed systems such as Signal Processing hardware.