It's a really great way to set up a simple login form and get rid of the ugly Basic Authentication prompt. You still use Basic Authentication (including a .htpasswd file or mod_auth_mysql, for example), but redirect using a custom 401 handler that shows a login form, that in turn sets the user:password combination as a cookie.
On the server, mod_auth_cookie then takes that cookie and fakes the Basic Authentication headers. It's literally so simple, it can be configured with one line on top of Basic Auth:
AuthCookieName CookieName
I've resurrected the module from the abyss, and hosted a shiny new homepage at http://modauthcookie.weebly.com/