A happenstance is a coincidental event. If you call your brother on the phone, that's intentional. If you bump into him in a restaurant, it's happenstance.
Happenstance is a combination of the words, happen and circumstance. Whereas circumstances are the conditions that surround an event, happenstance is the event itself. If you have no food at home so you go out to eat and sit next to a charming person who you end up marrying, your meeting was happenstance and your being hungry and having no food at home were the circumstances.