"Significant other" significa el novio o la novia de alguien (O el esposo o la esposa de alguien). En términos generales, significa alguien que es importante a alguien.

"What does 'significant other' mean? In what context does one use it?" "Significant other" is a euphemism. In order of socially recognized amorous relationships, marriage is first, then persons engaged to be married (fiancés and fiancées). "Signficant other" is a catch-all phrase that encompasses amorous boyfriend-girlfriend relationships and even less socially acceptable statuses, such as cohabitating couples and homosexual couples. Only rarely will "significant other" refer to someone who is engaged or married (e.g., "You and your significant other are cordially invited to Saturday's event," referring to the invitee's "significant other," which may be his wife, fiancé, girlfriend or homosexual boyfriend).

It's usually used to refer to someone's girlfriend/boyfriend or possibly even fiancée. I have never heard it used to refer to someone's husband or wife though. Just unmarried 'partner'. Eg. She is his significant other.