This is the 60th most frequent Russian word.
себя
"Себя" means "oneself" or "myself/yourself/himself/herself/itself" depending on the context.
In this sentence, 'себя' refers to the subject (he) in a reflexive way, indicating the object of seeing is the individual self.
Он видит себя в зеркале.
He sees himself in the mirror.
Here, 'собой', a form of 'себя', shows the reflexive action of feeling pride about oneself.
Она гордится собой.
She is proud of herself.
Here, 'себя' is used as a reflexive form to indicate that the feeling is experienced by oneself.