S.O. means "Significant Other." It can stand in for girlfriend, boyfriend, wife, or husband.
People will use that word if they do not know if you are married or not or whether you are interested in men or women. It keeps people from having this conversation:
"Your wife is a lucky woman"
"I'm not married."
"Then your girlfriend is a lucky woman."
"Actually, I have a boyfriend."
"Then your boyfriend is a lucky person."
"S.O." covers all of those situations.