Suppress weeds.
This is the one I like—less weeding! Some cover crops, such as buckwheat, grow so densely that they outcompete weeds—that's why they are sometimes called smother crops.
Others, like rye, oats, and sorghum-sudangrass (I call them the cover-crop “bad boys”) have an allelopathic effect on weeds—they actually exude compounds that suppress the germination of weed seeds.
Because these compounds can last awhile in the soil, it’s important to wait three weeks after tilling them under to plant your garden.