Let's consider a body
(that we will call the impactor) that travels in a
certain direction. This body is headed to impact with a second
body (called target body). The bigger the target is, the
more it will have a chance of being hit by the impactor.
This simple concept can be formalized introducing the geometrical cross section, which is the area occupied by the target body projected on a plane orthogonal to the direction of the motion. Therefore, this cross section is proportional to the chances of a hit.
If the target body has a non geometrical shape, its cross section will be the area projected on the plane orthogonal to the direction of the motion.