GayDays are an unofficial event centered around the first Saturday in June. LGBT people from all over the world come to the Orlando area to visit the parks and party.
For the Disney parks, yes...the parks are open to everyone...they are just a regular day in the parks with a large number of gay people and their families/friends in attendance.
There are also some private ticket events that you will need special tickets for, if you decide to attend them. I've never done any of the private ticket events, but I can hear the dance music at OKW from the Typhoon Lagoon party.