Iceland lies atop the Mid-Atlantic Ridge which runs north-south, right down the center of the big blue ocean. It's where two earth plates are pulling away from each other, and like you would expect from any wound that is constantly reopened, magma scars have built up, forming the ridge.
Iceland was born of this great crack in the earth's crust and as such is also pulling apart. A fissure runs the length of the island, very visible at places like Þingvellir, birthplace of modern democracy.
Earthquakes and volcanoes, then, are simply growing pains.