A 'balanced' engine is an engine constructed of components that are as evenly weighted as possible. This allows the engine to operate with as little vibration as possible.
For example, if you rotate a shaft that is heavier on one side than the other side, the shaft will "pull" towards the heavy side. This is how the vibration mechanisms in pagers and cell phones work - by spinning an unevenly weighted shaft on a motor.
This sort of an effect is generally undesireable in a automobile engine, and most manufacturers try to make the rotating components as symmetrical as possible. Larger components, such as crankshafts and flywheels, must generally be very close to ideal to prevent unwanted engine shake in consumer automobiles. Unfortunately, economics often dictate that less-than-ideal parts be used, and some engine vibration is generally tolerated.
In general, to balance an engine, all of the rotating parts need to be balanced - sometimes individually, and often as a set. This involves removing material from the 'heavy' side of the rotating components, either by drilling holes, or machining off some material. Special machines are often used to spin the components at the operating speeds, to identify which sides are the 'heaviest' on the complex mechanical shapes used for today's engines. In other cases, components are matched, by weight, to each other. Tolerances on such matching generally stay within 1/2 of a gram.
The net result of a balanced engine is generally a smoother-operating engine, sometimes with a touch more power output than before. It is often performed on racing engines, which require not only peak power output, but are frequently stripped of the other mechanisms that would normally reduce engine shake and noise. It is a labor-intensive and sometimes expensive procedure.
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