VPS hosting is a service offered by many cloud computing services, as well as other websites across the internet.
VPS stands for Virtual Private Server, and it essentially means that you can rent a portion of a server in a datacentre. This is the reason why, when purchasing a VPS, you can configure how much RAM, CPU cores and storage the server gets.
While you only get a portion of the server, that portion is yours and yours only. Nobody else gets access to that portion of the server, unless of course, you give them access to it.
Alternatively, you could also purchase a Dedicated Server from one of these companies, which allows you to rent out the entire server rather than just a portion of it.