Comment What Flex Is. (Score 5, Informative) 45
On a more complex level, Flash based Flex applications are robust interactive SOA applications with the ability to easily hook into various data services (JMS/Messaging, AMF[POJOs,OpenAMF via PHP, Coldfusion CFCs], XML over HTTP, and WebServices/SOAP).
So you can make rich desktop like applications with all the great stuff like drag and drop, interact with video, webcams, microphones, key events like CTRL and Function keys. Thin clients, where the app loads once. But have the deployment ease of a web application, and are platform agnostic (unix,mac,windows,pdas,cellphones,etc....).
Though the best way to see what it's all about is to look at live applications on the web:
http://maps.yahoo.com/beta/Yahoo Maps
http://www.thoughtfaqtory.com/flex/mxnaviewer/mai
http://weblogs.macromedia.com/pent/flickr/PhotoSe