What is "brain sex"? I am not going to google it for fear of the results.
“Brain sex” is pretty much the idea that, just as their is such thing a “male” body and “female” body, there is also such thing as a “male” brain and ”female” brain, and, just as male bodies and female bodies are different, male brains and female brains are also different (these differences are not often explained in a way that is any near as consistent as the way physical differences between males and females are described, however).
In relation to trans issues, the theory then goes that, in a vast majority of people, their brain sex and body sex are the same. However, in some individuals, their is a mismatch, which is how you get transgender people. It’s important to note that believers of this theory are emphatically against the idea of gender being a social construct.