What's your Android version? I'll assume you're using 4.1 or newer.
The .swf extension is used by files played by Adobe Flash Player. Unfortunately, Flash is not supported on Android since 4.1.
You can try installing the Flash Player APK. The latest version is for 4.0/ICS, but some people say it works on 4.1+/JB as well. Remember: Your Mileage May Vary™.
Additionally, Chrome for Android never supported Flash - even with the APK installed. (Thanks to Compro01 for confirming that!) So you'll need to use a different browser.
If you are not using Android 4.1 or newer, please update your question with more information.