Mushrooms are fungi, or rather, the reproductive part of fungi that live in the soil. Most of the time, the fungi just stay hidden, breaking down organic material. But when conditions are right, they burst forth, like desert flowers blooming after a rain. Mushrooms spread spores into the air and then go away when the sun comes out or the soil dries up. 

Aerating your lawn can help improve drainage, which will, in turn, help decrease the moisture that encourages mushrooms. It also helps to increase the amount of oxygen that gets to the roots of your grass. If you have excess thatch in your lawn (over half an inch), you have a lot of organic material that absorbs moisture and acts as mushroom bait. Dethatching your lawn can also help keep mushrooms away.

Mushrooms are an indication that your yard has a lot of organic material in the soil. Mushrooms help break down that organic material and make your soil more productive. If your shade and drainage aren't real problems, you can always just knock the offending mushrooms over and wait for the sun to come out.