A person's significant other is that person's partner in a relationship. The term is not gender specific; nor is the term specific to heterosexual ("straight") relationships. Thus, it can refer to a gay man's partner (as one example).
The term can be taken in the most positive, appropriate way by any listener. This makes it a polite term to use in any circumstances, particularly if knowledge of the other person is minimal.
The term also dances around the whole issue of marriage, since in the West, many people in relationships live together without being formally married. (At least, more than in the past.) Also, homosexuals are still barred from formally marrying in many locations. This further increases the use of the term significant other without risking rudeness or insult.
Example: "Tracy, do you have a significant other in your life?"