Star Trek - George Takei and Nichelle Nichols

I'll try and explain it as best I can.

By responding "neither" to the term "fair maiden" she's saying she's neither "fair skinned" nor a "maiden." I think in a lot of old fashioned media "fair" typically meant "a fair skinned woman" who was usually white, and "maiden" means "an unmarried young woman" who would also likely be a virgin. So by saying she's "neither fair nor a maiden" she's saying "I'm black and I'm not a dainty virgin."