Significant other (SO) is way of saying a person has a close relationship. Deliberately, it does not say what the relationship is.
It refers to a person's partner, but says nothing about marital status, relationship status, or sexual orientation. Similar terms, but more specific, are: sweetheart, better half, spouse, domestic partner, lover, soulmate, or life partner.
The term is now often used in invitations, such as to weddings and office parties. In correspondence from hospitals, for example, "you may be accompanied for your appointment by a significant other". "Relevant other" is another ways of saying the same thing. "Significant others" is sometimes used.