There is no Atlantic Plate; rather, this Ocean covers a broad basin that opened (and is still opening) between the North American, Eurasian, South American and African Plates. The rifting process began about 160 million years ago and continues today along the Mid Atlantic Ridge.
In such rift zones, where continents are pulling apart, the crust thins, the Earth's mantle bulges toward the surface and volcanism develops. Volcanic rift zones are evident in some regions of our Continents today: the Rio Grande Rift of North America and the East African Rift are prime examples. Eventually, as happened with the Atlantic, ocean waters will invade these rift basins.
Iceland began to form above the Mid Atlantic Ridge during the Miocene and emerged from the sea about 16 million years ago; its northwestern half lies on the North American Plate while its southeastern half lies on the Eurasian Plate. Volcanism continues along and near the rift line, adding more land to this island nation as it expands outward. The current eruption in south Iceland, which began yesterday, is from a volcano that had been dormant for 189 years; since it lies within a glacier-covered highland, there is a significant risk for catastrophic flooding.