Just what exactly Flash has to bring to the table.
Animations
This has always been the strong suit for Flash. Flash templates or Flash web designs look much more live and make the webpage stand out from the others largely because of animation effects.
Vector Graphics
Vector graphics are so well received simply because they look highly detailed and unaliased regardless of the screen resolution you have or how you resize the image. This is due to the fact they are not image files like .jpg or .png, but rather portions of code that are rendered immediately in the web browser. That's because of vector graphics that Flash templates have all the crisp and clean animations and smooth lines and borders.
Video
Embedable movies on Youtube and web pages is merely yet another thing Flash is popular for. Now again, the Flash makes it no big difference what operating system you have - videos or animation are going to be rendered beautifully, the only thing you need is deploy the Flash player plugin.
Compatibility across Platforms
Out of all the well-known web browsers Flash templates are supported on most of them. The fundamental idea and the best thing about Flash is that a simple browser extension makes Flash viewable in the same way across the majority of the modern web browsers, no need to say that the major ones - Internet Explorer, FF, Chrome and Safari render Flash effortlessly.