The United States occupied Cuba after winning the Spanish American War in 1898, and kept it as a colony until 1903. When we granted them independence in 1903, one of the stipulations was that we got Guantanomo. It not only gives us defacto control of Cuba militarially, what it was originally for was to give us a choke point to prevent foriegn navies from passing thru The Florida Strait and attacking the entire Gulf Coast. Legally, as a military base it is under direct juristiction of the President, making it a handy little spot to put people one wishes to be beyond the reach of the domestic courts.