The effect was discovered in 1857 by Louis Pasteur, who showed that aerating yeasted broth causes yeast cell growth to increase, while conversely, fermentation rate decreases.
The effect can be easily explained; as the yeast being facultative anaerobes can produce energy using two different metabolic pathways. While the oxygen concentration is low, the product of glycolysis, (pyruvate), is turned into ethanol and carbon dioxide, and the energy production efficiency is low (2 moles of ATP per mole of glucose). If the oxygen concentration grows, pyruvate is converted to acetyl CoA that can be used in the citric acid cycle, which increases the efficiency to 36 moles of ATP per mole of glucose. Therefore, about 18 times as much glucose must be consumed anaerobically as aerobically to yield the same amount of ATP.
Under anaerobic conditions, the rate of glucose metabolism is faster, but the amount of ATP produced (as already mentioned) is smaller. When exposed to aerobic conditions, the ATP production increases and the rate of glycolysis slows, because the ATP produced acts as an allosteric inhibitor for phosphofructokinase 1, the third enzyme in the glycolysis pathway.
So, from the standpoint of ATP production, it is advantageous for yeast to undergo Krebs Cycle in the presence of oxygen, as more ATP is produced from less glucose.
All the processes used in alcohol production are kept in anaerobic conditions, while breeding yeast for biomass is done in aerobic conditions, the broth being aerated.