A virtual private server 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 server’s 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. You choose how much resource you need – processor cores and RAM – when you buy.