Work is defined as force acting through distance. When force is constant, work is obtained as the product of force and displacement. If the force is changing, work is obtained as the integral of force over displacement. This integral is the area under the force displacement curve.
Summarily; if the force, F, acting on an object is plotted on the y-axis, the distance moved is plotted on the x-axis what we have is a force-displacement graph. This is useful because we can find the work done by (or on) a system by finding the area under this force-displacement graph.
Hence, the area under a force-displacement graph usually shows the work done as explained above.
