WebDAV is a file-transfer protocol, similar to FTP in that it is used to upload/download/modify files collaboratively on the internet. It is the access method of choice for the CIT-IS LAMP hosting environment, because it allows users to use their CUWebLogin credentials to get access to their LAMP accounts, while still keeping file ownership and permissions on the server side consistent, so multiple users can safely share access to and collaborate on a LAMP account.
The two popular options for using WebDAV in Windows are the Microsoft built-in DAV client, and WebDrive, a commercial offering with a lot of neat features.
WebDAV is based on HTTP, so while WebDAV URLs can be accessed in browsers like Firefox, Internet Explorer, and Safari, those browsers don't actually support the WebDAV protocol for actual uploading/downloading of files. What will usually happen if you visit a WebDAV share in a browser is that you'll see the contents of the WebDAV share served as if they were a webpage - such as getting the code for your index.php file, instead of the processed PHP output.