The Young Men's Christian Association was founded in London, England by George Williams and a group of Evangelical Christians. They were concerned by the fact that the young men coming into the city thanks to the Indutrial Revolution didn't have any healthy outlets and activities. They were going to brothels and pubs to let off steam and falling into sinful ways.
The first YMCA opened in the United States in Boston, December 1851, after having expanded to Australia, Canada and other countries. In 1855 the YMCA adopted the philosophy: "build a healthy spirit, mind, and body for all". They realized that they would be serving females as well, but they kept the name the same.
During the 20th Century focus seems to have drifted (in the United States, at least) more to healthy mind and body, rather than more of the spirit. At this point, they seem to concentrate more on athletics, but still keep programs such as day care and youth education going very strong. At the same time, the YMCA has strongly espoused international political goals such as gender equality, sustainable development and fighting racism and HIV/AIDS.
And, of course, the YMCA is the home of everyone's favorite Disco song.
YMCA - Wikipedia
World Alliance of YMCAs
United States YMCAs
YMCA (the song) - Wikipedia