A virtual private server (VPS) is a way of hosting files and apps in a data centre. Like a dedicated server, it gives you your own resources: processors, memory and storage.
It’s different to a dedicated server in that you do not ‘own’ a specific piece of hardware. Instead, portions of a physical server are allocated to different users. Whatever these other users do, it can't affect your VPS performance. It’s an isolated private environment for your own use.
A VPS is different to shared hosting in that you are guaranteed hosting resources and you’re free to install any software. You choose these resources when you buy a VPS.