I know it is pretty late. But just wanted to put in my two small cents here.
The original concept of cloud computing was a utility-like service that would provide a pool of shared resources for clients to use on-demand – thereby allowing customers to leverage a large pool of resources without having to bear the burden of the capital cost of building or maintaining the entire infrastructure themselves. In the web hosting world what we refer to as “cloud computing” sometimes aligns with this original concept, sometimes not so much, depending on the service in question.
All cloud products that are offered as a web hosting service have one thing in common: they are virtualized. "Virtualized" means that your “server” (whether called an “instance”, “slice” or something else by your service provider) is actually a virtualized operating system (kernel) that is referred to as a “virtual machine”, or VM. The VM is running inside a “container” system, which is in charge of managing the resources of multiple VMs running alongside yours. There are several products that do this, some of which you may be familiar with – some of the more well known products out there are VmWare, VirtualBox, and XEN.