Could you use it in some contexts and explain a little of its meaning? Does it have an usual use in every day socializing?
It's a more deferential way of asking "Do you have X?". Saying "do you happen to have" adds a level of uncertainty about it, suggesting that the person you're asking isn't actually expected to have X, but there's a chance they may. It's quite common in everyday speech, although really never necessary.
"Do you happen to have the time?"
"Do you happen to have a spare pencil I could borrow?"
For both of those, the phrasing suggests that it'd be nice if you did have the time or a pencil, but it would be a lucky chance (happenstance) if you actually did.