The Galápagos are located on the very northern edge of the Nazca plate, which is bounded by the Cocos (north), the Pacific (west), the South American (east), and the Antarctic (south) platesThe Nazca plate itself is currently drifting south, away from the Cocos plate, and east, away from the Pacific plate. Since the net direction of drift is southeast, the Nazca plate is colliding with the South American plate. At the point of collision, the South American plate, which is made of light continental crust, is riding up over the Nazca plate, which is made of dense oceanic crust. This type of plate interaction is called subduction.
As the Nazca plate is forced into the mantle, it melts and its melt products work their way up to the surface to form volcanoes. The land is further raised by the crumpling effect as the western edge of the continent rides up over the descending plate. The result of all of this is the Andes, a young, highly volcanic, rapidly growing mountain chain. This same movement of the Nazca plate is responsible for producing the cluster of volcanic islands we call Galápagos.