You could think of the sites that share your server as your roommates; there's really not that much separating you from them. Sure, you can close the bedroom door, but they can still cause nightmares for you in the kitchen and the bathroom. In web hosting terms, all the sites share a single server's resources, so huge traffic spike on Site A may impact the neighboring sites' performances. It's even possible that another site could take down the shared server altogether, if it crashed hard enough.
An example here is the rapidly growing trend of "inbox zero." It's actually known by a variety of names, but it refers to the practice of keeping your email inbox count at zero stored emails. Essentially, it's dealing with every email as it comes in and then deleting or archiving each one so that your inbox is always empty. This boils down to a fundamental shift in how users are utilizing their email inboxes.