ColdFusion Extensions (CFX) are ColdFusion custom tags that are written in Java or C++. Unlike CFML custom tags, CFX tags come in handy when you want to do something that isn't possible with traditional CFML code.
A perfect (and understandable) example of the use of ColdFusion Extensions is a custom tag that generates thumbnails of images. Obviously, with traditional CFML, you have no way of modifying the source image and generating a new, smaller representation of that image. With CFX tags, however, you can harness the power of other, robust languages (such as Java or C++) to give your ColdFusion applications all the power of those languages as well.
CFX tags are also the perfect way to incorporate functionality into a ColdFusion application that you've already written in C++ or Java. By encapsulating this functionality into a CFX tag, you enable ColdFusion developers to use this functionality at any point within a ColdFusion application by referencing it as a CFX tag.