Hotlinking is the act of pasting an image link into a post/signature/avatar that they haven't hosted themselves. Most people will save an image that they like, and then upload it to a hosting service like Imageshack (my avatar, as an example), and on Not606 I believe that you can upload it to the site itself. Hotlinking skips that step and just involves linking to the original image, which can cause problems; beyond the downsides of doing it from pernicious sites, if someone catches you hotlinking (which uses their bandwidth) they can do tricky things like switching the image at that link location, which means that your lovely picture of Bea Arthur could turn into bestiality or some such.
Bears noting that there's a good possibility that it isn't a virus; if someone is hotlinking to a black-flagged site -- even if nothing nasty actually gets off-loaded on to the user's machine -- it will often cause the antivirus program to react.