In the United States the term is sometimes used in invitations, e.g. to weddings and office parties. In this context, a person and their significant other might not be cohabiting and might not be engaging in sexual relations. For example, a person's fiancé(e) would be considered a significant other, without any assumptions regarding living arrangements or sexual activity before their marriage. Conversely, it is assumed that some sort of steady connection exists between the invitee and their significant other, i.e. the event for which the invitation is extended won't be their first date.
The first known occurrence of the term was in 1953 by U.S. psychiatrist, Harry Stack Sullivan, a former editor of the journal Psychiatry, in his posthumously published work, The Interpersonal Theory of Psychiatry. While the term currently enjoys use and familiarity, many people find the term irritating due to its lack of specifics and adoption by pop culture. Greatest use of the term peaked in the late 80's to mid 90's and has generally declined since then if favor of other terminology as deemed appropriate.
In social psychology a significant other is the parent, uncle, grandparent, or teacher - the person that guides and takes care of a child during primary socialization. The significant other protects, rewards and punishes the child as a way of aiding the child's development. This usually takes about six or seven years, and after that the significant other is no longer needed, the child moves on to a general other which is not a real person, but an abstract notion of what society deems good or bad.