Gay Pride is a movement that celebrates the GLBT community. This movement emerged in the 1960s. It came out of a time when mainstream society tended to view being GLBT as something shameful or inferior to being heterosexual.
The term "Pride" was deliberately chosen counter the idea that there was something embarrassing or wrong with being gay.
In many places, Pride occurs in June to commemorate the famous Stonewall riots. These riots occurred in 1969 as a response to homophobic raids that were happening at gay bars. During raids, police would drag people off to jail on fake charges, even if they weren't committing crimes.
But on June 27th, 1969, GLBT patrons of New York City's Stonewall Inn had had enough and fought back when police tried to arrest them. This culminated in what are often called the Stonewall Riots. These are seen by many as the birth of the Gay Rights Movement.
Many communities refer to June as "Gay Pride Month" and hold Pride Parades and other events during this time.