Hi,
What is Flex?
Flex is a way to make SWF files!
At the heart of Flex is the ability to create SWF files that run in Adobe Flash Player. Distill all the features down and really it is a development paradigm that compiles to SWF. It really is that simple but often we make the definition much harder. Just like Flash can create SWF files, so can Flex but the way you develop is completely different.
Flex is for developers.
Flex was not built for animators, writers, accountants; it was written for software developers and the paradigm matches the development methodology you already know. If you know Java, C, C++, C#, Delphi, VB, PHP, ColdFusion, Python, Ruby, you can learn Flex with little effort. The goal when Flex was created was to make a development paradigm that developers could learn easily matching the methodology they already know yet create SWF files for Flash Player (and now AIR). Flex has classes, components, a compiler, a debugger, class libraries, and uses XML (MXML) for declarative markup of components. The ActionScript programming language is based on ECMAScript 4 (the language standard behind JavaScript) and has full support for the ECMA XML scripting standard E4X. It also has most of the UI components that you already use ( like button, list, datagrid, combobox, and tree) but it also supports containers like HBox, VBox, TabNavigator, TitleWindow and many others. If you have written software before you can learn Flex easily. Better still is that Flex is compatible with all HTTP servers, version control systems, and any server side programming language, so the knowledge you have of servlets, php, ASP.net, or JSP is really handy. Flex just lets you program the client side in a paradigm you already know and understand.
Flex is for making applications...
Flex was built for making rich client side application behavior. It wasn't built for making web pages, banner ads, or server side logic it was built for creating client-side applications that run over the Internet talking to remote servers. Flex has been used to make some really great apps like Buzzword (Document Editor like Microsoft Word but in the web) or Picnik (Photo Editor/Manager for touching up your best snapshots) or SlideRocket (Presentation software like Apple Keynote but in the web) or Oracle Sales Prospector (An enterprise ERP application. Yes Oracle uses Adobe Flex! ) or many other applications you can see at Flex.org. The real key is that all these examples provide an application experience just like desktop software.
that run on the web (Adobe Flash Player)...
Flash Player 9 is installed on more than 95% of computers that use the Internet and has been installed more than 3,500,000,000 times at a rate of over 10,000,000 times per day. When you develop software, you want it to run compatibly in as many places as possible. Adobe Flash Player provides a solid foundation to build these experiences without the need to install or update anything on the end users computer. If you were running a store you would want that store available to as many customers as possible and choosing Flash Player allows you to provide a great experience (rich) to 95% of the web (reach). Make sure to look at the reach of the technology you select, if you choose something not widely installed or incompatible, you are simply turning away customers and business.
For more detail check this links:
http://en.wikipedia.org/wiki/Adobe_Flex
http://www.kirupa.com/developer/as3/whatisflex.htm