Shadows are an important way to add realism to a scene.
There are a number of trade-offs possible when rendering a scene with shadows. Just as with lighting, there are increasing levels of realism possible, paid for with decreasing levels of rendering performance. Shadows are composed of two parts, the umbra and the penumbra. The umbra is the area of a shadowed object that isn't visible from any part of the light source. The penumbra is the area of a shadowed object that can receive some, but not all of the light.