Hi
VPS or Virtual Private Server is a collection of virtual servers hosted on a physical machine. They act similar to dedicated servers but they have lesser capacity and power. However they're cheaper than dedicated servers are.
Because it is a collection of servers it could be confused with shared hosting. However unlike in shared hosting, VPS or VMs (Virtual Machines) don't share their server resources with other users.
Although virtual, it is also different from a cloud server in that, while VPS are hosted on one physical machine, cloud servers are hosted on a virtual space that was created by integrating a vast network of physical machines.
VPS are hosted on physical machines by deploying a "hypervisor" which can manage all the VMs separately.
Hope this helped.