The air-fuel ratio is, simply, the ratio (by mass) of air to fuel. This number most commonly comes into play when talking about combustion, primarily in the operation of gasoline-fueled internal combustion engine-driven vehicles. The stoichiometric ratio of air to gasoline is 14.2 to 1; this is the ratio at which there is precisely enough air and fuel that when the fuel burns, all fuel and all air will be consumed in the reaction. As this is the most efficient burn ratio, it also produces the maximum possible power.
Rich and lean air-fuel ratios both take power away from the engine and can do damage. Rich air-fuel ratios cause less than 100% of the fuel to be burned, increasing hydrocarbon emissions (unburned gasoline) and reducing heat. Excessive fuel may wash away some lubricating oil, causing scoring damage to the combustion cylinders. It may cause fuel to burn in the exhaust manifold, raising exhaust temperatures and damaging catalytic converters. Lean air-fuel ratios can cause premature combustion or pre-detonation which results in severe physical stresses to the engine, and overheating. The "ping" noise heard during a pre-det condition is the sound of the pistons vibrating sideways in the combustion chamber as combustion attempts to force them down while they are still moving upward.
The air-fuel ratio is typically monitored by the ECU using an oxygen sensor which, when heated, produces an output voltage corresponding to the density of oxygen ions in the exhaust stream. The computer will constantly adjust the mixture richer or leaner based on what the oxygen sensor says in order to approach stoichiometric combustion. It can also be monitored by the driver with an oxygen sensor connected to a gauge or voltmeter, as is common in auto racing applications.