From wikipedia :
Web Distributed Authoring and Versioning (WebDAV) is an extension of the Hypertext Transfer Protocol (HTTP) that allows clients to perform remote Web content authoring operations. (...)
The WebDAV protocol provides a framework for users to create, change and move documents on a server, typically a web server or web share.
In other words users that work with the server that implements WebDAV can share, move and edit files through a web server. There is also a way to lock file or get a specific revision of it. WebDAV is supported by many client applications like windows Explorer or Nautilus. It is similar to another protocol- FTP. FTP is faster, but it doesn't run on top of HTTP. WebDAV also support SSL and authentication.
CardDAV and CalDAV are extensions to WebDAV that enable client/server address book and to accessing the calendar on the remote server.