Straight people use this term... the non-bigoted ones anyway. :-) People used to say "my special friend" or "my better half" or "the one I love" or "my lover", but now it's "my significant other" you hear most often. It is used to identify a person's most special (significant) partner/lover/mate.
A good example of its usefulness to straight people: Let's say a woman is not divorced from her husband, but separated with divorce pending, and now she has found a new love interest she is very serious about and will likely marry. That makes the new love intererst her significant other.
No, they don't have to be living together.
I've never heard it refer to a child - that would not be appropriate!
It is a "politically correct," all-encompassing term indicating the person with whom one is in an intimate relationship: Husband, Wife, Girlfriend, Boyfriend, Spouse, Lover, Male, Female, Same sex, etc. It does not refer to one's children.
It's what gay people use to refer to one another. (that are in a relationship). Straight people DO NOT use this phrase.
Your love interest, your domestic partner.
No, you don't have to be living with your significant other. 'Significant other' simply describes the person with whom you are romantically involved.