When I first heard this term it was in a movie or a TV programme. I understood from the context that it was a specially trained team, but I didn’t stop to ask what it stood for; according to wikipedia it’s “Special Weapons and Tactics”.
The term seems to have crept into business language, and taken on the meaning of a special project team brought in to solve an urgent problem. They generally have a a single focus to solve the problem and a stronger mandate to get things done. Which does make we wonder; why not just give the existing team the power to solve the problem in the first place – perhaps before it even became a problem.
Often the existing team has no capacity to address a big new issue, or they may lack the knowledge to make a change. Here’s Obama talking at this year’s SXSW about making government more digital, he put in place a “Digital SWAT Team” to make this happen (from about 9.30 to 15.00).
In this case it’s clear that the knowledge brought into the US government services was able to address the problems of legacy systems, and outdated knowledge. They had the mandate to act, supported by the most powerful person in the country – of course they could get stuff done.