How are volcanic islands created by the motion of crustal plates over the mantle?

Volcanic islands are formed as a crustal tectonic plate containing an ocean moves over a magma hot spot. These hot spots are actually in the mantle, while the tectonic plates are all in the crust (hence "crustal"), so the hot spot stays in the same place while the plate moves over it. This magma carries an enormous amount of heat, and it can then be released into the crust and create magma chambers there.

These magma chambers build up over millions of years and then finally erupt into volcanoes. They start at the sea floor, erupting lava directly into the sea which rapidly cools and hardens into rock. Over many eruptions (or sometimes a few very long slow, continuous eruptions), the rock builds up in layers, until eventually it can reach the surface.

Once the rock starts reaching the surface, it forms land, and that is what we call a volcanic island.

Volcanic islands are often formed in chains, as different parts of the plate are exposed to the magma hot spot in sequence.

Because of their mode of formation, volcanic islands usually have gradually sloping terrain and rich soil, making them very good for farming.