A computer (server) that stores the information about a website or an application and then sends the information to a visitors computer when they type in that particular web address. There is free and paid web hosting. Most free web host are limited in their capabilities, do not have longevity, and require a minimum number of visitors for the account to remain active.
Shared Hosting: sharing the same server with others.
VPS Hosting (Virtual Private Hosting): the same as a shared host except you have a lot more control over the server and you share it with much less other clients. VPS servers is a pseudo server that has controls as if you are controlling the entire server except you are actually controlling only one segment (container) of the server. Extremely busy websites and very high traffic need a VPS server.
Dedicated Server: an entire server (computer) that you have total control of. You can turn it on and off, reboot it, install new software, and use Windows or Linux commands to execute programs just as if the computer was in your home.
For more information see: http://en.wikipedia.org/wiki/Category:Web_hosting