The “Flash swf widgets” include flash slideshows, flash intro’s and banners intended for web use. Flash is a flexible but also an expensive program to learn as well as to maintain. Thats the reason it has become a little less popular in recent years. Other options have appeared with a broader range of possibilities at a lower cost both financially and time-wise. Then again, there are still many websites that use Flash swf widgets because it makes sense from an SEO point of view or because users demand them on their sites.
An example of this would be real estate websites using pre-made flash slideshow dynamic pages to show photos and details about houses for sale while the user scrolls down the page automatically watching the pictures go by.
These web apps are not made to be installed on a site, they are more like a small part of a website. If you want to see flash examples in action I recommend the following companies: 20 Second Test or Fotosearch
Weaknesses of Flash swf widgets:
Flash is expensive and takes time to learn. There are many new technologies that have come up over the past 10 years such as CSS3 and HTML5 that can create graphics just as nicely but also provide far more flexibility than flash ever will. Search engine optimization favors static html pages over dynamic flash widgets since its easier for crawlers to index them for relevant keywords.