Magma rises from the mantle because it is more buoyant than the surrounding rocks. This occurs when gas dissolved in the magma forms bubbles, reducing its density and causing it to well upward. If the magma finds a vent, or the pressure cracks the crust, it can reach the surface.
The material that makes up magma consists of molten rock as well as dissolved minerals and gases. Under normal circumstances, the pressure of the rock around a magma pocket is enough to keep those dissolved elements in solution. However, if the rock fractures due to tectonic activity, it can reduce the pressure enough to allow the gases to come out of solution and form bubbles. When this happens, the magma begins to exert upward pressure as it tries to reach the surface.
If there is a natural vent available, the magma may simply seep to the surface in a slow, controlled flow. However, if there is no readily available vent, the upward pressure increases until the magma flow fractures the rock above it. When this occurs, the sudden release of pressure can create a volcanic eruption. The material carried to the surface can even begin to build a cinder cone around the vent, producing a brand new volcano.