Clear Spheres can be purchased from the Monster Arena owner after you do most of his jobs for him (which means you unlocked all of the Area/Species Creations). The Clear Spheres are green in color. They remove nodes from the grid. Not recommended that you use them until AFTER you fill up the SG, which should take around 20 hours if you played straight through. You also cannot use these on abilities, so don't worry about losing Curaga/Hastega/Zombie Attack/w/e.

Stat creation Spheres are purple, and you get many of these throughout your adventures. When you go into the SG section on the Main Menu, you can head to an empty node, and when it prompts you to use a node, (in the same way you improve your characters) you can use the purple ones, which creates a new stat node in the empty node.

When a node is created, it acts just like all of the other, preplaced nodes, except that it gives the highest possible bonus that you can receive. +4 in stats, +40MP, or +300HP.