Winning all that's on offer in a sports competition, e.g. all the tricks in a game of bridge, or the all the major competitions in a sport in a single year - especially associated with tennis and golf. More generally, any all-out achievement.
The term originated in the game of bridge. Charles Jones, in Hoyle's Games Improved, 1814 explained what slams are in bridge:
"These declarations will supersede that of Boston [winning the first six tricks] simply... The highest, called Grand Slam, is undertaking to get 13 tricks."
It is most widely known nowadays as the name for the feat of winning all the four major tennis competitions in one year. It is widely reported that the American journalist Allison Danzig brought the term grand slam from the card table to the sporting arena, when using it to refer to the achievement by the Australian Donald Budge in 1938. Budge was the first player to win all the major singles tennis competitions in one season and it was widely reported as his 'grand slam'. The term had been used before to apply to a tennis achievement. In October 1933, Alan Gould, the Associated Press Sports Editor wrote this for the Fresno Bee Republican:
"Crawford, already the holder of the Australia, French and British singles championships, will make his bid for the first 'grand slam' in tennis when he plays Perry tomorrow afternoon for the American title."
Perry in fact won the match.
In fact grand slam had also been used for some time prior to that in the sports of golf and baseball. In baseball, a grand slam is a home run hit with all the bases occupied. In golf it is the winning of all the season's major championships - as in tennis. The first person to achieve a grand slam - in the 'winning all major championships in one year' sense, rather from the specialized baseball sense - in any sport was the golfer Bobby Jones.
The Daily Northwestern, November 1930: In the closing year, 1930, he [Bobby Jones] had accomplished the impossible - the grand slam of golf - by winning all four major titles.
The Syracuse Herald, October 1922: "If the Pirates should happen to win it would be the dizziest grand slam by which the Giants ever lost and they have been up against a few in their time."