To support collaborative authoring, the original specification of WebDAV included file locking, but it punted on the "versioning" part of DAV due to the complexity of the revision tracking domain. DeltaV (RFC 3253), the versioning and configuration management piece of WebDAV, was defined later. Searching capabilities were also added in a later extension (RFC 5323).
If you encounter a WebDAV server referred to as "class 1", that means it lacks locking. Class 2 includes locking. A WebDAV server with versioning is often just called a "DeltaV" server.
Most operating systems file managers' user interfaces include an extension to present and manipulate WebDAV folders and files as if they were local. These include Windows file Explorer, macOS Finder, and GNOME Files (Nautilus) and KDE Konqueror on Linux.
In each case there will be a "connect to server" option where you provide the WebDAV server's URL (the URL format varies from tool to tool, sadly). You then provide the username and password for accessing the server.
Wikis usually use a simplified markup language that's much more limited – and quicker to grasp – than HTML. A wiki engine lives in a webserver like WebDAV. To permit a vanilla web-browser to edit, wikis don't include the ability to edit multimedia files, and the only "file/folder management" that's included is the ability to create and modify hyperlinks between wiki pages.