I'm trying to get this girl to go out with me, but she said to her friend that for her I am like a gay best friend. What does that mean in other words?

Basically a gay best friend is a friend that's a guy but has a girly attitude. Your not in the dating zone for her because gay boys are a lot like girls and girl to girl are like best friend and sisters.  Maybe that's what she thinks of you  - a sister.