A day on which women ask men out. (This assumes that the reverse is usually the way of things.)
Comes from the Li'l Abner comic strip in which the rich father of the ugly Sadie Hawkins organized a day in which unmarried women could run after available men and drag them back to a shotgun wedding. This was needed to keep Sadie from becoming an old maid. Cletus the Foetus tells me that "The original 'Sadie Hawkins Day,' in the Li'l Abner strip, was November 16, 1937 (though Al Capp, the cartoonist, resurrected it on random days in November in following years)."
The most common date for celebrating it these days, at least as found in my net searching, seems to be November 9. (rougevert commented: "how odd. here (australia) this happens on the 29th of February.")