Seafloor spreading happens at the bottom of an ocean as tectonic plates move apart. The seafloor moves and carries continents with it. At ridges in the middle of oceans, new oceanic crust is created. The motivating force for seafloor spreading ridges is tectonic plate pull rather than magma pressure, although there is typically significant magma activity at spreading ridges.
At the Mid-Atlantic Ridge (and other places), material from the upper mantle rises through the faults between oceanic plates. It forms new crust as the plates move away from each other. The new crust then slowly moves away from the ridge. It is a place of earthquakes and volcanos. Seafloor spreading helps explain continental drift in plate tectonics. At oceanic trenches, seafloor crust slides down and under continental crust.
Earlier theories (e.g. by Alfred Wegener) of continental drift were that continents 'plowed' through the ocean. The modern idea is that the ocean floor itself moves and carries the continents with it as it expands from a mid-ocean ridge. Today, it is accepted. The phenomenon is caused by convection in the weak upper mantle, or asthenosphere.
Additionally spreading rates determine if the ridge is a fast, intermediate, or slow. As a general rule, fast ridges see spreading rate of more than 9 cm/year. Intermediate ridges have a spreading rate of 4-9 cm/year while slow spreading ridges have a rate less than 4 cm/year.