A Virtual Private Server (VPS) is a virtual server which is set aside for your sole use. No other customers will have access to it. In layman’s terms, a server is a powerful computer that stores all of the data and files that make up your website. When someone types your domain name into their web browser, that powerful computer “serves up” your website to the searcher’s screen.

Now for the virtual aspect: VPS uses virtualization technology to split that one powerful server we just talked about into multiple virtual servers. Think of it this way: it’s one piece of physical hardware that functions like several separate servers.

The word private means just what it implies. Your virtual server is reserved for you, so you won’t have to share RAM, CPU, or any data with other users.

(Taken from DreamHost’s VPS page – https://www.dreamhost.com/blog/beginners-guide-vps/)