It is thought that convection currents in the Earth's mantle rise to the base of the lithosphere where the divergent plate boundary exists. This supplies the area with copious amounts of heat and pressure that melts rock from the asthenosphere (or upper mantle) that then travels to the rift area forming large flood basalt flows. Each eruption occurs at only part of the plate boundary at one time but when it does occur it pushes the two opposing plates slightly away from each other (at an average rate comparable to how fast human fingernails grow).
Over the course of millions of years the plates will grow many hundreds of kilometers in a direction away from the divergent plate boundary. Therefore rock closest to the boundary is younger than rock a great distance away on the same plate.
Continental crust is often split in two by divergent plate boundaries.