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.