Clear Spheres are special spheres that are aqua in color and cannot be dropped, stolen from, or bribed from monsters. They will allow you to clear any stat node on the Sphere Grid, which will negate whatever stat increase that node gives. The only way to get these is by buying them from the Monster Arena shop, but they won’t be available right from the beginning of unlocking it. You will need to capture at least five of every single fiend in the game (those that are registered in the actual Monster Arena) before they become available in the shop, where they will cost 10,000 gil each. Note that ability and locked nodes cannot be removed with Clear Spheres.
What makes Clear Spheres so great is the fact you can remove the stat nodes that only increase a stat by one or two points, then use a purple sphere of the corresponding stat to place it on that same node. So, you would be getting a net gain of 2-3 extra stat points there. This won’t be needed to complete the main story, but you will want to do this when taking on the superbosses.