Hi. I can’t give you an exact identification, but I suspect you are dealing with some sort of puffball. These mushrooms belong to the family Agaricaceae and get their name from their shape (spherical - essentially lacking a stalk) and the way they disperse their spores: through a hole in the top, which puffs them out if the mushroom is stepped on. Your fungus seems to lack a stalk, and it also seems to have a hole in the top. I suspect they look a bit rough because they are near the end of their lifecycle. The U. of Nebraska has a nice, short article on them here. It notes that these tend to appear in the late summer or early fall and that they are beneficial decomposers. This article from the U. of Illinois is also good, and it provides some advice for improving the look of your lawn if you have them, though there isn’t any way to eliminate them completely. I’d also recommend this Buckeye Yard and Garden Online article from a few years ago that discusses them and some of the animals that can associated with them.