Smocking is the technique of creating a series of pleats and then stitching these pleats together at certain points in order to create designs.  Honeycomb smocking is a type of smocking where the end results give you a beautiful diamond design.  Even if you don't know the name, this design may still look familiar and I think most of us associate it with renaissance style.  Honeycomb smocking may have been more common then, because it allowed the fabric to shrink and expand before the invention of elastic.  It involves hand stitching, which means it can be time consuming, but you can see that effect of these stitches make for an unique embellishment.  The pleating will cause fabric shrinkage so I think in most cases, it's best to do this before doing any project construction. You can really do your honeycomb design any size that you wish and you'll notice as you work, the fabric will naturally begin to pleat above and below the design.  If you're wondering what do it with these pleats, I would just press them flat so they look more like an inverted box pleat.