The first sort of plate boundary is called a divergent boundary, or spreading center. At these boundaries, two plates move away from one another. As the two move apart, mid-ocean ridges are created as magma from the mantle upwells through a crack in the oceanic crust and cools. This, in turn, causes the growth of oceanic crust on either side of the vents. As the plates continue to move, and more crust is formed, the ocean basin expands and a ridge system is created.
Divergent boundaries are responsible in part for driving the motion of the plates.
As you can imagine, the formation of the new crust on either side of the vents would act to push plates apart, as we see at the Mid-Atlantic Ridge, which helps to move North America and Europe further and further apart. Mid-ocean ridges are vast mountain chains in the ocean and are as tall if not taller than mountain chains on land. The process which actually drives the motion at these ridges is known as convection. Magma is pushed upwards through the ridge cracks by convection currents. As some magma erupts out through the crust, the magma which does not erupt continues to move under the crust with the current away from the ridge crest.