According to the theory of plate tectonics, how do two plates interact to form chains of islands called island arcs

Islands form an arc when two oceanic plates converge (come together, approach) creating a row of islands above the overriding plate. The older, heaver plate gets forced below the lighter plate. That old plate heats up and descends into the lithosphere. The edge of that plate begins to melt as it gets deeper into the earth. The melting plate feeds magma chambers that supply volcanic islands that forms an arc when the molten rock erupts onto the ocean floor of the overriding plate.