No they don't see what groups we have or even a list for all the titles in each group.
Once you assign your hubs to groups, the ones in each group are connected by "previous" and "next" links after the hub. Let's say you write hubs about how to take care of dogs. One is about grooming, one about food, one about choosing the right vet, etc. If someone is trying to learn about how to care for a dog before they get one, they'll find one of your pages. Once they finish reading that hub, they can go right to your next hub about dogs using those links. If those links aren't present, they may not know you have other hubs about dog care to read so they'll go back to the search engine and may not find your other hubs. I'm not sure how often people use those links, but a reader may stay on your pages longer if they can from one to another more easily.