Many sites utilize flash for their navigation buttons or for intros in order to impress prospective clients. Flash is very impressive if it is done well because it is visually pleasing while still loading quickly. Unfortunately, even though flash is very... flashy [ahem], search engines could never parse the content. It is basically a graphic and therefore just a bunch of pixels to a search engine so you do not want a website made completely of flash
Flash has been depreciated and will no longer be supported by any browsers in the near future. This has happened because of the popularity of Apple's i-devices such as the iphone and ipad. Apple and the company who makes flash, Adobe, do not get along very well and because of that Apple simply never supported flash content on their i-devices... ever. Initially this was a draw back for Apple, but has ultimately lead to new technology and scripting languages such as HTML5 and CSS3 which will ultimately replace and surpass flash in the long run.
The long run has come and gone. Flash has completely gone the way of the Dodo bird. If you still have flash on your website, you need to update it asap. Schedule a meeting with one of Your-Web-Guys using