Cloud hosting comes in two general flavors. Public and Private.
With the public cloud you buy a slice of a server that is shared with a number of other clients or tenants. A private cloud is a more secure cloud based environment in which only the specified client can operate.
The purpose of either cloud is to achieve coherence and economies of scale, similar to a utility (like the electricity grid) over a network. At the foundation of cloud computing is the broader concept of converged infrastructure and shared services.