Anaerobic respiration happens when there isn't enough Oxygen available for Oxidative Phosphorylation to occur. Without Oxidative Phosphorylation, ATP synthesis occuring across the inner mitochondrial membrane stops, as does ATP synthesis in the Krebs cycle. Therefore, in order to meet it;s energy demands, the yeast uses anaerobic respiration to keep Glycolysis going, yielding 4 ATP molecules (Net: 2) per Glucose molecule converted to Pyruvate.
It works by allowing by allowing NADH to dump it's hydrogen, allowing it to reform NAD, which is again used to oxidise glucose to pyruvate, yielding ATP. I think this is best illustrated diagramatically.