An engine mount is the part that holds the engine to the body or to the engine cradle (sub-frame) of the car. In a typical car, the engine and transmission are bolted together and held in place by three or four mounts. The mount that holds the transmission is called the transmission mount, others are referred to as engine mounts.
Moreover, to reduce the engine vibration felt inside the car, engine mounts are filled with rubber so that there is no direct metal-to-metal contact between the engine and the car body. To further dampen the vibration, some engine mounts are filled with liquid. Some car manufacturers (e.g. Toyota, Honda) use active vacuum-controlled engine mounts that vary dampening as needed. Porsche offers electromagnetic mounts to actively reduce engine vibration transferred to the body.
However, an engine mount doesn't need any maintenance or regular servicing. It only needs to be replaced when it fails or wears out. For many cars, an engine mount is covered by the Powertrain warranty.