When you look at the known mistresses of European royalty, most of them are members of the court or daughters of prominent families in the era.

For example, when you look at some famous mistresses, few, if any, were "common" or prostitutes - Rosamund Clifford (mistress of Henry II of England) was the daughter of a wealthy Marcher Lord. Bessie Blount and Mary Boleyn who were rather famous mistresses of Henry VIII (and by extension, Anne Boleyn and Jane Seymour. While unproven to be "mistresses" per se, they were chosen as wives while Henry VIII was still married to someone) were both daughters of wealthy men who were in favor of the King and part of his court. Sadly, many of these mistresses served as maid-of-honours to the Queen, and thereby caught the King's eye. (I got this information from years of researching Tudor England. Recommended books and sources of information is at the end of this reply.) A King in Medieval Europe couldn't risk going to a common brothel - threat of harm or assassination, disease, and bastard children with an "embarrassing" woman was not worth it to most people in the aristocracy. It was much easier and safer to catch the eye of a maid or courtier.

I'll refrain from expounding on every known royal mistress in Medieval Europe (plus I can really only confidently speak of English history. As you can imagine, the list is rather large.) But the pattern is consistent - a young, beautiful, woman in court catches the King's eye and the having the affections of the most powerful man in their world was rather appealing to many ambitious women.

I'd recommend reading "The Six Wives of Henry VIII" by Alison Weir - it gives great insights on late medieval England and the courting practices of Henry VIII. It includes a lot about his mistresses, and that's where most of my knowledge comes from. Weir also has a book exclusive to Mary Boleyn - "Mary Boleyn: the mistress of Kings" which also a great read. More on royal mistresses can be found in Dennis Friedman's book "Ladies of the Bedchamber: the Role of Royal Mistresses"

Every mistress is different, but they all have a fascinating history.