A manhole cover is a plate used to close off a manhole -- typically an access point to underground utilities.
In modern cities, much of the infrastructure is subterranean, such as water/sewer lines, electrical lines, communication lines including phone and data lines, etc... Often access is required to permit someone to repair damage, remove outdated equipment or to install additional equipment.
Access to these tunnels is often through a manhole. These are usually cylindrical in shape as the circular cross-section is best suited to handle the compression stress of the surrounding earth.
The access is often circular due to the shape of the access tunnel. The manhole cover then is also circular.
Another reason many manhole covers is circular is that this shape will not fall into the hole no matter its orientation. Compare this to a square, which can be lined up across the diagonal and dropped through the opening.
Manhole covers are often heavy metal plates. They serve to keep out unauthorized people as well as protect the access tunnel. They must be heavy enough to withstand traffic rolling across them without deforming, so are often cast from cast iron. Since this means that they will be heavy, another reason for them to be round is it can be easy to transport by rolling.