Adding a fabric frame to a pillow simply means that the needlepoint has strips of fabric sewn to the side. The edges of the fabric can be mitered (so they point out from the corner) or sewn straight (they are straight with the edges). This helps the design stand out from any edge treatment and also helps anchor a particular color in the design. One, two, or multiple fabric frames can be used to "build out" the design. The pillow is then backed as normal.
Finishing a pillow without a fabric frame makes the design stand on it's own. If the design is large enough to be it's own cushion this will work. You also need areas where your eye can rest (the blue triangles in this case).
I finished both these pillows this weekend.