There is actually more than one right answer to this:

1). It is impossible to drop a round lid into a smaller round hole (the manhole cover sits on a lip in the ground, so the cover is actually bigger than the hole).  

2). Also, if a round shape is turned or flipped over, it still keeps the same length across its center. If you used a square, rectangle, hexagon or any other shaped lid, it could be rotated and fall into the hole.  Note that an equilateral triangle will not fall into the hole either (this is a triangle that has an equal length on all 3 sides).

3). Also, a round manhole cover weighs less than other shapes, since it can be made with less materials than other shapes, and still allow a person to climb in and out of the hole.  It may take 2 people to remove a square manhole cover, but only takes 1 person to remove a round manhole cover.

4). A round cover can be moved by rolling it on its edge. 

There are other answers, but these are the most common.