The term Airsoft is often used to refer to an object, and a sport.
Airsoft guns are detailed replica firearms. They look (and often function) very similar to the real weapon they are modelled after. At first glance, they look perfectly real, but upon closer inspection it is apparent that they are made out of plastic or cheap metal. Typically, air power is produced by compressed gas or a spring to propel a 6mm BB out of the model's barrel. Various manufacturers, mostly in the Pac Rim, create these models for hobbyists to collect and use.
Motivation for buying an Airsoft gun over the genuine article can be due to the fact that the "real steel" is illegal in the owner's country, too expensive, or too deadly. Many hobbyists also enjoy modifying the internals to upgrade the power, or have the model resemble one of the owner's favorite weapons.
The sport of Airsoft uses these models. Various games similar to paintball can be played: skirmishes, siege games, capture the flag, and full-scale military simulations. The participants in the game often deck themselves out in full military gear for extra realism.
Airsoft attracts many people interested in milsim, and relies heavily on the honor of the participants. Unlike paintball, the pellets fired by the guns typically do not leave a visible mark, requiring people that were hit to call themselves "out" and face whatever penalty the rules dictate.