Answer: It represents the area of the two circular sides ("lids")
Explanation:
Imagine you made a cylinder out of 3 pieces of paper. The cylinder can be decomposed into two circular shapes (radius r) and one rectangular piece with two side lengths: one is "h", the other has to be long enough to go around each of the disks, so it has to be 2*pi*r long.
So the term 2*pi*r*h is the area of the rectangular piece and pi*r^2 is the area of each of the "lids" Since there are two of those, the term 2*pi*r^2 represents the area of the bottom and top lids.