To drive rifting some kind of extensional force is required to stretch the lithosphere.
Ultimately all tectonics forces is the Earth are the result of mantle convection, and the extensional forces required for rifting are no exception. Mantle convection arises due to thermal expansion of mantle material upon heating. The expansion causes a reduction in density in comparison to the overlying fluid and the resulting buoyant forces cause the material to move upwards. Once it reaches the suface it cools and becomes more dense and sinks. Heating then occurs and the process repeats itself to form what are known as convection cells.
Mantle convection can explain rifting simply by placing continental rifts at boundaries of convection cells. It is unlikely that all rifts are the direct result of mantle convection, as is impossible to derive set of simple cells that is compatible with the geometrise and locations of all modern rifts. Thus, other forces must also be at work.
Rifting can be caused when hot material from a mantle plume reaches the base of a continental plate and causes the overlying lithosphere to heat up. In addition to this the uwards movement of the plume against the base of the plate results in extensional forces, which can cause rifting.
Slab Pull and Ridge Push
As a continental plate is subducted, the material in the subduction zone tents to pull the plate downwards, creating a force known as slab pull. Material build up at spreading ridges tends to push the two plates away, creating a force known as rigde push. Slab pull and ridge push can cause rifting when two ends of a continent is subjected to these forces. If the continent contains a weak zone, these forces can be sufficient to cause continental break-up.
Subduction may also cause rifting when the lithosphere bends prior to subduction. The bending increases the curvature of the plate which means the surface radius of the plate must increase, putting the plate under extensional forces which can result in rifting.
Rifting may also be apparent in areas of thickened elevated continental crust, such as those that result from collisional orogeny (mountain building). In these cases, the weight of the material causes lateral spreading due to gravitational collapse, and because of the spreading stretching and rifting occurs.