Client/server architecture
If you want to categorize Flex applications, you can say that Flex applications follow SOA architecture model, where Flex is used to create the client and you connect the client to data using services.
Let’s go back to browsers and how web applications are delivered. When the browser makes a request, the server uses a combination of static content (HTML/CSS/JS code) and scripts (these scripts may query a database or call other scripts, but in the end they output HTML/CSS/JS) to prepare a page. This page gets loaded and rendered by the browser. A key element here is that, usually this page (or response) has the presentation markup and the data baked into the same message.
When a new state of the application is to be presented, the browser makes a new request and the server prepares the page. The client “just” renders the data.
Flex applications works differently. The server sends the compiled Flex application (the SWF file) that runs inside the browser using the Flash Player plug-in. Usually, this SWF file holds only the client-side business logic. If data are need (from a database for example) the Flex application makes a request for those data. The server sends only the data (this can be in XML, JSON, AMF3 format), and the client knows how to represent this data visually. What we have here is a service oriented architecture: The Flex application is the client―a client that can consume data services from the server. The application can change state without refreshing the page or reloading the SWF file in the browser. The application is a client that can do more than “just” render data. Thus using Flex and Flash Player it is possible to create almost anything that makes sense to deploy on the web, from games to applications, to widgets that are integrated within “classic” web applications, and more.