Which area of the world is the most prone to volcanoes?

A volcano is an opening in the surface of planet Earth (or any other planet). Through this opening, molten rocks and gases emerge from deep interiors of the planet. The volcanic eruption can be gradual or violent, depending on the pressure built up underneath it. 

Volcanoes are typically found at the edge of the tectonic plates. That is, at the plate boundaries. Earth's core is composed of a number of fragments, each called a tectonic plate, all of which float over a liquid layer underneath them. Volcanoes are generally found at the diverging and converging boundaries of these tectonic plates. 

Volcanoes can also be found in the middle of the tectonic plates due to volcanic hotspots. These are fixed regions of hot material discharge from the core-mantle boundaries. As the tectonic plates move over them, we get new volcanoes while old ones become dormant. The Hawaiian islands are an example of these volcanoes.

Thus, regions where plate boundaries or hotspots exist are more likely to have volcanoes. An example of this is The Ring of Fire, an area with an especially high amount of volcanoes. The Ring of Fire mostly follows the perimeter of the Pacific Plate.

Hope this helps.