Coordinates are a method to describe the shape of objects by numbers.
When you have got a set of coordinates, you can re-create the object from these data. They describe an airfoil by single points and each point is defined by a pair of x-y coordinates. The airfoil can be made up from 50 or 100 points, which mean 50 to 100 coordinate pairs. As the designer of an airfoil does not know, how large the airfoil will be on your real wing, he must select an arbitrary airfoil size. The units are of no importance, as the airfoil has to scaled to the desired size anyway.