Planishing is the final smoothing of the metal surface. At this point you are only getting the dings out that were made in the surface during the raising process.
Planishing is tedious and is achieved by many light hits with a fairly flat faced hammer. Here you will want to strike the metal where it contacts the ball stake. One should hit just hard enough to begin evening out the nicks and dings. If you strike too hard it will thin the area and possible distort the shape.
If you polish the face of your planishing hammer you will avoid adding blemishes and dirt into the surface of your armour. This also helps you better see the areas you have gone over as those areas will be shiny. The smoother you get the surface the less sanding you will need to do later and thus lessen the risk of thinning the finished piece. I find that closing my eyes and running my fingers over the surface often reveals areas needing work my eyes missed.
The fact that there are only two pictures dedicated to planishing should not give one the impression this is a quick task. Planishing is very time consuming.
The planished surface will have many shiny facets.