VPS hosting works through ‘virtualization technology’. Simply put, virtualization technology is what enables the division of one server into multiple individual private servers.
Each VPS is like an independent private room within a massive house. Each room is capable of being used independently by individual users/websites, without the need to share any ‘rooms’.
What this means, is that each website will have access to it’s own RAM, storage, bandwidth, etc., without being affected by what happens to the other ‘rooms’ or VPS’s.
On the other hand, shared hosting is when your website is hosted on a shared server, utilizing common resources and capabilities across multiple websites.