It means equal treatment. It started as a movement in the 70's when gay marriage was illegal in most of North America. The Gay Rights movement has continued into the modern day defending the rights of the LGBT (Lesbian, Gay, Bisexual, Transsexual) community as assholes like Bush move to officially restrict them to second-class citizenship.
Here are a few links for you to check out.
Why Gays Are Second-Class Citizens In Repair
Marriage Benefits
Benefits of Civil Unions
I hope they answer your question.