There are special softwares that can divide dedicated servers sources into seperate pieces. Each piece can have its own ip and identity. There forewe can say its a method of partitioning a server such that each partition is one idendity and act like a server it self.

Usually VPS is a middle solution between expensive dedicated server or unable reseller web hosting.
With VPS you have more tools to control.

Lets say you have a server 16 GB ram and 8 core processor and 1000 GB disk space. You can have 8 virtual server 1 each has 2 gb ram 1 core processor and 125 GB web space. There is a main VPS software divides the sources these pieces. With VPS comes nearly all controls you have on a sperate dedicated servers such a ssh access, setting own dedicated software, dns records etc etc.

Usually VPS's machines uses special web hosting control panels. For example Cpanel has special softwares for VPS. There are more to know on VPS but this is a seperate post issues.