Seeing "Guest" for the first time. Problem?

I am embarrassed to ask a question like this because I am sure it is common knowledge, however, I have never had anything other than just one computer that I am the only user of. I am using Windows 8. Where I live, there is a wireless connection that is shared by many users. The WiFi router was not set up with a password, so anyone can connect who is within range. This situation is not really new, and I am not aware of any problems, however I saw a "Guest" in the file explorer (see attachment). What bothers me is the implication of the name Guest. I do not want any Guests on my computer! That implies that they have access to files on my computer? When I clicked on the name I received a message that they declined my invitation to join their homegroup (or something like that). Worried that I may have accidentally done something wrong by initiating contact, so to speak, I clicked advanced network settings and turned off network discovery which I was thinking would make us not visible to each other. And, no, I have no idea whether that was a good idea or not. I do know that 2 of the 3 guests disappeared, but one did not...

...should I be worried?

Any info at all would be greatly appreciated!