Flex is a nice way to create client side applications. It can run as a
stand-alone "SWF" application, but if you want to interact with any types of
data that exist on a server, you need a server interface. Most Flex programmers
use ColdFusion server to allow that interface to the data on the server. You
can move, create, and alter files, access database servers, and create
PDF/Flash Paper outputs using ColdFusion.
ColdFusion is basically the least expensive server interface option (and the
simplist in my opinion) for Flex.
I should note that Flex cannot do everything ColdFusion can do as Flex
requires a server interface for the above mentioned. Once your applications
require data from the server, you will need an interface. ColdFusion can do
almost everything that Flex can once you incorporate AJAX technologies, but
because AJAX is a js/xml/html/css combined technology - it does suffer the bugs
of various browsers where Flash (or Flex) is a compiled "swf" file that, in
theory, is more platform robust once compiled.
Hope this answers your question.