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.
A domain must be unique (for example there can only be one single Yahoo.com) and must be registered with a domain registrar (ie. NameCheap); while for sub domains, users can freely add it on top of the existing domain as long as their web host provide the service. Some would say sub-domains are the ‘third level’ domains in the sense that they are simply “sub folders” under the domain root directory, normally used to organize your website content in different languages or different categories.
Many services offer a low "starting price," but require you to prepay for two or three years of service to get that price. After the promotional period, the renewal price for some services can be two, three, or even four times the initial promotional pricing. While the initial deal might be incredible, the cost of transferring your site (or paying the added fee) in a couple of years may be something to consider.