brother-in-law
A man who is your brother through marriage, not birth.
A brother-in-law is someone who becomes your brother through marriage rather than birth. This happens in one of three ways: he's your sibling's husband, your spouse's brother, or the husband of your spouse's sibling.
If your older sister marries someone, that person becomes your brother-in-law. If you have a brother and he gets married, his wife becomes your sister-in-law, and you become her brother-in-law or sister-in-law. The same connections form through your spouse's family: when you marry someone, their brothers automatically become your brothers-in-law.
The term works the same way regardless of gender. If you marry someone who has a brother, that brother is your brother-in-law whether you're male or female. The in-law part simply signals that the relationship came through marriage rather than blood.