A Flash applet is a small application that runs inside the Flash web-browser plugin. Flash is an application created by Macromedia (now owned by Adobe) that can create media presentations containing text, images and sound in a file that can be played by the Flash plugin.
Where to get the Flash Plugin
You can download the Adobe Flash player from Adobe's website.
Odds are, you already have the Flash plugin installed. Unfortunately, many advertisers are now generating flash content, so a web browser that has the Flash plugin will see more ads.