In this passage of Jane Eyre, the word mortify has a Christian connotation. Motify usually means to make somebody feel ashamed or embarrased, but also to subdue something through punishment or discipline.
In this context, when he talks about mortifying the lusts of flesh, he is talking about ending the sinful nature of lust and sexuality as part of a process of santification, through discipline or even punishment chastising the body to submission.