It is a 'hot spot' - an upwelling of magma within the mantle that manages to penetrate the (relatively) thin oceanic crust to form a volcanic sea mount.
Where these sea mounts rise above sea level - a volcanic island will appear.
They are often found in 'chains', since, compared with the movement of the oceanic plate, these upwellings are realtively static. As the plate moves over the hot spot, new, active islands are formed, whilst those furthest away have long since passed over the hot spot will be less active or extinct.
Hawaii is just part of the long, continuous Emporor Sea Mount - Hawaiian Ridge chain that extends all the way from the Aleutian Trench - though not all sea mounts penetrate the ocean surface to form islands.