Synchronous condensor is just a synchronous motor without any load , but with over excitation.
Generally it is used in receiving grid electric substations to improve power factor.
The synchronous condensor gives leading var and improves the power factor of the system like condensor (capacitor) thats why it known as by this name.
During heavy loads, voltage and power factor at receiving end substation tends to lower. Synchronous condensor is operated with over excitation and supplies leading vars or draws current at leading power factor to improve voltage and power factor profile of the system.
During low loads, receiving end substation voltage increases due to line capacitance. Synchronous condesnor is operated with under excitation and consume reactive power from the system. So voltage profile improves.
Now a days the use of synchronous condensor has been stopped. In place of synchronous condensor , static var compensator (SVS) are being used.
Static var compensator is nothing but a combination of capacitors, reactors and thyristors . Thyristors is controlled to turn on and turn off the capacitors and reactors to control power factor and voltage.