Next time you put your foot to the floor to accelerate away from a stop, or motor on up an of-ramp, take a second to fully appreciate what's happening. All the power created by the miracle of internal combustion going on inside the engine is smoothly making its way to the ground without the vehicle rattling itself apart from vibration, or the engine twisting its way through the hood. Despite the engine's best efforts to twist itself out of the engine compartment, the process of acceleration is largely uneventful thanks to the system of motor mounts holding the power plant firmly in place.
One end of the system bolts tot he engine, and the other end is secured to the vehicle frame or sub frame. Along with holding the engine in place, the motor mounts have another equally important function. They isolate the surrounding steel from all the vibration and shaking going on as the engine makes power. The motor mounts simultaneously hold things down and allow for movement. Save for a few very fancy viscous fluid or hydraulic type systems, most motor mounts accomplish this feat with just two metal parts bounded together with a rubber insulator in between. The rubber holds the two metal mounting points together and also allows for a small amount of movement while absorbing engine vibration and preventing it from reaching the rest of the vehicle.
Just like tires, kick balls, floor mats or anything else made of rubber that takes a beating, motor mounts can also wear out and fail. Time and thousands of stops and tarts take their toll on the rubber holding the metal of the motor mounts together. The rubber can crack, become spongy or just plain fall apart. Liquids leaking onto the mounts itself will accelerate the process. Oil, power steering fluid, transmission fluid, or and other leaking liquid falling down ont the engine mount will speed it demise.
Engine power modifications in conjunction with overly spirited driving can also overcome the original design specifications of the motor mount and cause torque-induced motor mount failure. If there's a whole lot of shaking, thunking and clunking coming from under the hood when you put the pedal to the metal, then it may be time to inspect and replace the motor mounts. If the engine is small, a good two-handed push or heave-ho may reveal way too much movement, and daylight shining through the two halves of the broken mount.
Larger engines will require a jack and various blocks of wood in order for you to check for broken motor mounts. If a broken or cracked mount is found, chances are the others have been overstressed and are on their way out as well. Also keep in mind that, along with the usual two engine mounts, their is a third cousin, the transmission mount.