Here you go, better than I can do:
Cover crops can provide erosion control, weed suppression, add nitrogen to the soil, reduce soil compaction among other things. The idea is to have the ground covered all year or nearly all year with some type of vegetation. Usually it’s planted in the late summer or fall with more winter hardy plants. It can be drilled in, broadcast spread or even aerial seeded. I cover crop in my gardens. It keeps the weeds down and adds a lot of organic matter to the soil during the off season.
Plants like vetch and clover can add a lot of nitrogen which saves fertilizer expense. Using less chemicals is usually seen as a good thing if you can cost effectively have an alternative. Stopping soil erosion is important too. Good topsoil is impossible to replace unless you want to wait a few lifetimes. There’s a few guys in my area that plant rye in the fall as a cover crop, burn it down in the spring, roll it down and drill beans into it. If it’s a wet spring they sometimes have a hard time getting it terminated and the field stays wet longer. That’s a good thing on a dry year. I guess each person needs to do a cost:benefit analysis and see if it’s right for them.
I see you’re in N WI correct? You might be able to get crimson clover and hairy vetch started yet this fall. I attached some pics of my “crimped” vetch from this spring. It was terminated with the gator tires and made a nice thick mat. I would suggest not tilling it unless you want to spend a lot of time cutting stuff out of your tines.
It's inexpensive fertilizer, compared to the cost of traditional fertlizer.
That's the main reason we do it. Plus, because I use the tiller on the potato field in the spring it helps to rebuild the soil, tillers are actually very harsh on soils. Now, if you go to our corn field, which used to be more rocks than dirt, we have started a process of three loads of manure from the farm down the road, then winter rye cover crop and lighter tillage in the spring. In the past few years we have built the soil back up to point where now we can go out and just pick rocks that still surface, in years past we would have gone crazy trying to pick all of the rocks.
There's a lot going on in the soil that we don't see. The cover crops can not only add nitrogen (if they are legumes) but more importantly they give beneficial soil organisms structure and food so the soil continues to build. Erosion and tillage destroy the soil structure, erosion for ever and tillage until plants are able to mitigate the damage. Ultimately, cover crops help build carbon in the soil which is used by the organisms in the soil.
You might want to take a good set of soil samples including micronutrients and organic matter so you have base line data. Then as you start to work on the soil, it will be really slow so having the data to show you are going in the right direction will be encouraging.
