And for what shadow volumes are: It is basically an imaginary volume that encloses the shadowed area on your world. For example a sphere produces a cone shaped

And for what shadow volumes are: It is basically an imaginary volume that encloses the shadowed area on your world. For example a sphere produces a cone shaped shadow volume behind it when a point light hits it. In computer graphics you can use this geometry to render shadows on object. Imagine a ray coming out from your eye, if that ray first hits a shadow volume and then an object then that point of that object is inside shadow. If ray never hits the volume or passes through volume