Your mate, spouse, husband, wife, boyfriend, girlfriend, steady and/or lover. Used when you don't want to be too specific, or when the details are nobody's business.
Why's Roger always talking about his significant other? Why don't he just say girlfriend?
Combination of "statistically significant" and "significant other."
Since he spent twice as much time with Karen as with any of the other girls he was dating, his friends called Karen his statistically significant other.