The United States National Tactical Officers Association definition of SWAT is, "A designated law enforcement team whose members are recruited, selected, trained, equipped and assigned to resolve critical incidents involving a threat to public safety which would otherwise exceed the capabilities of traditional law enforcement first responders and/or investigative units."
SWAT teams were reportedly first created in the mid-1960s, when Philadelphia Police Department decided to create a specialized task force to deter and stop an increasing number of bank robberies in the city. The Los Angeles Police Department soon created their own SWAT team in 1967 to prepare for large-scale unrest or widespread violence in the wake of the Watts Riots.
During the War on Drugs in the 1980s and 1990s, the SWAT team concept spread throughout the country, and soon police departments in every U.S. state had SWAT teams with heavy equipment purchased through grants and overstock from the Department of Defense to tackle what they saw as an increasing threat potential.
In addition, the FBI has its own SWAT team that is used for situations that local police may be ill-equipped to handle. They handle high-risk situations from hostage rescue to protection of visiting foreign dignitaries.
Countries other than the U.S. often have their own counterparts to SWAT, such as Germany's GSG-9 or the United Kingdom's SCO19.
In Video Games
In games where the player is to fight (or even play as) the cops, a SWAT team will often make an appearance to give the player a greater challenge than just fighting the regular cops. They will be better armed and fight with greater efficiency forcing the player to try and match their skill.