Ozone is a special form of oxygen. Normally, two atoms of oxygen form an oxygen-molecule. Contrary to this, an ozone molecule consists of three oxygen atoms.
Once this molecule is decomposed, new reaction partners are needed. All effects which ozone has on the biochemical course of reaction in the aquarium are based on its high oxidation power. Ozone is the strongest available oxidation agent. On the other hand ozone is environmentally friendly, as it only consists of three atoms of oxygen and it doesn't introduce any chemicals into the aquarium water.
Just as in nature ozone is formed in a flash inside the ozone electrode from the oxygen content of the air. Therefore, three oxygen molecules are needed to form two ozone molecules.