Custom Filter AA, or CFAA for short, is AMD implementing non-box filters that look outside the pixel being processed in order to calculate final colour and antialias the image. The sample resolve for that is performed on the shader core, data passed in so the programmable hardware can do the math, with the filter function defined by the driver. That means AMD can implement a pluggable user filter system if they want, but even if they don't they can update, add and remove filters from the driver at will whenever they see fit.
The big advantage is the ability to perform better filtering than the standard hardware resolve. However the disadvantages include possible implementation of bad filters, and speed issues because the driver now has to issue, and the hardware run, resolve calculation threads which chew up available shader core cycles.