A lamp with size 0 will give you a very sharp shadow:
As you increase the lamp's size it will give you much softer shadows.
What you are increasing is the Penumbra
from Wikipedia:
The umbra, penumbra and antumbra are three distinct parts of a shadow, created by any light source after impinging on an opaque object. For a point source only the umbra is cast.
A: Umbra
B: Penumbra
The penumbra (from the Latin paene "almost, nearly" and umbra "shadow") is the region in which only a portion of the light source is obscured by the occluding body
An illustration using a mesh as emitter:
A small light source=sharp shadows, most of the light is blocked by the object:
A larger light source=softer shadows, the light source is only partially blocked:
