If your site becomes too busy for shared hosting or VPS, you may need your own dedicated server.
A dedicated server is a server whose resources are entirely dedicated to your site. None of the server resources are shared with any third parties.
Usually the maintenance of a dedicated server is your responsibility however some hosts offer managed dedicated server solutions – at a price.
You will need a dedicated server if your site becomes very busy and the resource requirements are greater than that provided by a shared hosting service.