How does the  Web Player work?

The web player encompasses Windows Media Player, Real Player, and the Flash player. It writes the appropriate html code for your page based on the properties you set (either while designing your form or during runtime).

The web player may be set-up to choose the appropriate player based on extension of the media file to be played (Automatic player type) or the developer may specify the player.

What's the advantage over just using a regular media player?

Because its properties may be set from server-side code, this player goes where the others don't. It is very easy to use, and the ability to set properties at runtime allows you to have your server-side (.Net) code control the player!