Virtual web-server hosting
Virtual hosting is a method for hosting multiple domain names (with separate handling of each name) on a single server.
You can simple put the HTML-files, or PHP, ASP, ... on the server via FTP (or even beter secure copy).
Most provders will also provide a connection to a database, if you request.
But you will not be able to install your own application or services. For that you need a Dedicated server.
Versio.nl is a great hosting provider with hosting-plans that start from € 4.99.