The idea is simple: If you sign in to a Wi-Fi network on your Android phone, your Chromebook will automatically know the password as well. This works in the other direction, too. The devices share Wi-Fi credentials as long as you’re using both with the same Google account.
In order to use Wi-Fi Sync, you’ll need to connect your Android phone to your Chromebook first. Set up the “Phone Hub” feature to get your device connected (and to get access to a few other handy features).