GAF is an acronym for Give a Fuck. Hence, a low GAF level indicates that the bearer feels answerable to very few. A high GAF level would mean that said person would be intimidated by an outside source and would try to exhibit more responsible behavior, language, etc.
A: I couldn't believe the things you were saying at last night's party.
B: Yeah, well, these days my GAF level is pretty low. I look forward to the day when it will be zero.