The general case is simple economics: it's suddenly vastly more worthwhile to try. Anything (or combination of things) that changes the risk to reward ratio spurs entrepreneurship. Drastic drops in risk generally mean that there would be few to no people with the requisite skills, since if something wasn't previously possible who would know how? Drastic changes in valuation are more likely to have a few daring individuals with some experience: it was possible before, but not worth it for many.
The other responses already cover some scenarios, which I include to be complete. Where someone else hasn't covered it, I'll provide an example:
On the risk side:
Couldn't get there
Locations previously inaccessible or non-existent. (several responses)
Another possible scenario: Drones. Perhaps cave systems are inaccessible due to the presence of toxic chemicals. A remote device could get in and out. Similarly, monsters which hunt by scent might not attack a drone.
Fall of an advanced civilization: A staple of the genre is the existence of some vastly powerful ancient civilization which falls to some horrible tragedy. The circumstances of the fall leave behind untold riches, etc... So immediately after the fall, those untold riches are suddenly available to those who would hazard the perils which destroyed that once proud empire from within.
Opponents unbeatable w/o new weapons. (covered elsewhere)
Couldn't carry the loot
The item of value was too dangerous to retrieve before. New containment techniques/materials significantly reduce the risk to life and limb. For example: The resource in question must be taken from a live monster. Once a reasonably safe way to trap it is invented, a new industry is born. Similarly, natural threats such as fungal spores or radioactivity, once understood, become possible to counteract.
New medical technology severely reduces the risk of death. For example: lots of monsters who carry deadly bacteria. Before antibiotics, a small wound became a death sentence.
On the reward side:
Wasn't worth it
Something is now worth going after that wasn't before. The new value could be in social influence rather than capital valuation.(covered)
The tools needed for the job get significantly cheaper. For example: mass production makes quality armor/weaponry widely affordable. So while you could get them before, they cost more than one could reasonably expect to earn over an adventuring career. This would be a great source of experienced veterans. "I remember when only respectable folk could afford a decent suit of armor to hunt wumpus. Now any peasant with more greed than sense is hacking up the undergrowth in scale and greaves. You want to learn the ropes? Fine, you deal with the riff-raff. I'm retired."
People with the required skills become more common. For example: An external threat leads to the training of a large army who ends up not actually having to fight . Now there are lots of combat-ready, armed, young adults just sitting around. This one ties well with the fall of an advanced civilization. For example: The army was raised to defend against the ancient and powerful empire when said threat destroyed itself or succumbed to an (un)natural disaster (rain of fire, "Do not call up what you cannot put down", etc...). Now there's tons of loot lying around if you can survive the radiation/army of the dead/demon horde/and so on...