Your guild support pool is the defense bonus for your GvG sectors. HQ gets the main defense, and the sectors surrounding it get whatever remains. Guild support pool is a combination of the support pool offered by your guild level, as well as any Saint Basil, Deal Castle, or Observatories on your guild roster and their current level. Basil and Deal offer 3 support pool per level, and Observatories provide 10 per level until level 10. I believe after level 10, observatories offer 1 support pool per level, but I am not definite on that.
Also remember that any sectors that are cut off from your HQ will not receive the support pool benefits.