Is there a plausible explanation for a large number of armed adventurers in a fantasy RPG setting?

I’m working on a Dungeons & Dragons setting. I’m looking for a comprehensive and logical explanation why, in a feudal society similar to Western Europe in the Middle Ages, there might be bands of armed adventurers (both male and female) wandering the country, slaying monsters, and frequenting taverns.

Does it follow that if you introduce magic and monsters guarding dungeons filled with treasure into a historical medieval setting, you’ll see an adventuring class emerge? Have there been any real world analogues to an “adventuring class” (obviously without the monsters and magic)?