I understand the meaning of the parable. Parables are, by definition, a simple story based on common knowledge. Because everybody is supposed to know the backstory, nobody bothers writing it down.
No, this is not generally the definition of a parable. They are not necessarily based on a story that is common knowledge or that is considered 'well-known backstory'. Though there are some of Jesus' parables that appear to allude to common knowledge (Luke 19:11-27 appears to trade on this common knowledge, for instance), the majority of them are simply short stories or situations which are generic in type and furnish the material for a major teaching point.
For this reason, there's no particular suggestion that there's a specific story behind the parable of the ten virgins (Matt 25:1-13), it does draw upon common knowledge of 1st century wedding practices, not all of which are necessarily well-known to us.
If there's something more particular you'd like to know here, please ask a follow-up.