Virtual Private Server (VPS) is a type of hosting that enables each website to function independently, as if it was working on a separate machine. Shared hosting server might cause problems when it goes down, as it is possible for all other websites on that server to go down with the server as well.
VPS is better because it gives you most of the options of a dedicated hosting server, but for a price of a shared server. If you see that your website has more to offer than a shared server can back, and on the other hand you don’t have enough assets to cover an dedicated hosting server, VPS is the right thing for you.