When we talk about Hosted Servers we are talking about a Virtual private server (VPS). A VPS is a marketing term used by Internet hosting services to refer to a virtual machine for use exclusively by an individual customer of the service. The term is used to emphasize that the virtual machine, although running in software on the same physical computer as other customers' virtual machines, is functionally equivalent to a separate physical computer, is dedicated to the individual customer's needs, has the privacy of a separate physical computer, and can be configured to run as a server computer (i.e. to run server software).
Long story short: a virtual private server is a cheaper alternative to having a dedicated server. You get the same service but your VPS is easier to upgrade, downgrade and quite possibly even sidegrade. Your slice of the shared community pie can be as individual as your company, tailored to your individual needs - without the expensive outlay for your own dedicated server.