To synchronize the files on your mobile device, you'll have to install the Windows version of AirStream and keep the computer and mobile device connected to the same WiFi network. Once you start the session on both devices, you can play all your PC files directly on the mobile device.
Browsing the files you have stored on your computer is as simple as selecting the location and opening the appropriate folder. There are two major shortcuts: the desktop and the download folder, since those are common places for important files.
To enjoy videos on Chromecast, you must have the app installed on your Android and open the videos following the same procedure for other applications such as YouTube. In this way, you can enjoy the multimedia content of your computer directly on Chromecast, transforming the mobile device into a sort of intermediary between the PC and the TV.