President Bill Clinton first declared June "Gay & Lesbian Pride Month" in 1999, but its roots lie in Christopher Street Liberation Day on June 28, 1970. Christopher Street Liberation Day was a demonstration to commemorate the police raid of and subsequent riot at Stonewall Inn, a gay bar on Christopher Street in Greenwich Village in New York City. The movement quickly spread, and demonstrations, celebrations, parades, and other gay pride events have been held annually in June (and sometimes other months) around the world.
The first Pride was a riot. Read this article from the Southern Poverty Law Center for a history of the origins of what we now call Pride.