In an English context, it means winning the English top division (now the FA Premier League, the old First Division prior to the inception of the Premiership) and the F.A. Cup in the same season. It was last achieved by Arsenal in 2002.
A complete list of seasons with The Double winning teams in England:
In auto racing, The Double is a term used for a driver on Memorial Day weekend attempting to race in two prestigous races on the same day, the Indianapolis 500 during the day and the Coca-Cola 600 during the night. Pulling "the Double" has only been possible since 1992, when the 600 began being held under the lights. Such an accomplishment can be very draining, with one driving up to 7 hours on a race track and also having to travel 430 miles from Indianapolis to Charlotte, where the 600 is held.
One-time Indy racer John Andretti first attempted the feat in 1994 and it has been done successfully by two other drivers since, Tony Stewart in 1999 and 2001, and Robby Gordon in 2002 and 2003. Stewart's double in 2001 is the only attempt which has encompassed all 1,100 possible miles. Gordon has also tried the double in 1997 and 2000, but rain plagued both attempts. The '97 Indy 500 was postponed by rain until the following Monday (eliminating a true "double") while the 2000 Indy 500 was rain delayed for 3 hours and prevented Gordon from officially starting the 600.
Also a novel by Fyodor Dostoevsky, The Double