Groups are a way to organize your campaigns. If you have multiple campaigns with similar content, or want to combine your campaigns by when they were sent, just group them together! A group reduces the number of pages you might need to scroll through to find an old campaign and allows you to select and work with similar campaigns, quickly.
These groups look different in your sidebar than a regular campaign. A group always has multiple thumbnails on the left, and a set of numbers, on the right. Notice that a regular campaign has only a single thumbnail, and no number to the right.