Island arcs are those well-known series of islands with volcanoes (such as the Ring of Fire). They are usually caused by tectonic plate boundaries passing over geologic hot spots in the Earth's crust.
Plates moving together cause one plate to go under another, and another to go on top. This makes a string of islands because the hot spots stay still while the plates move over them. Essentially the same phenomenon occurred in "dead" island chains like the Galapagos Islands, yet is still live elsewhere. All these chains are made by land moving over hot-spots in the Earth's crust, not by the hotspots moving. The position of a hotspot seems independent of tectonic plate boundaries.