A gully is part of a spectrum of landforms created as running water erodes sediment. Erosion starts with sheet erosion, until running water concentrates into small irregular channels called rills. The next step is a gully, like this example from near the Temblor Range. As a gully grows, the streamcourse would be called a gulch or ravine, or maybe an arroyo depending on various features. Usually none of these involve erosion of bedrock.
A rill can be ignored—an offroad vehicle can cross it, or a plow can wipe it out. A gully, though, is a nuisance to everyone except the geologist, who can get a clear look at the sediments exposed in its banks.