Both types of respiration release energy from glucose, but they differ in the oxygen needed, the products and the amount of energy released.
Aerobic respiration needs oxygen and takes place in the mitochondria. Glucose is broken down completely, so a lot of energy is released: glucose + oxygen → carbon dioxide + water.
Anaerobic respiration happens without oxygen, for example in muscles during hard exercise when oxygen cannot be delivered fast enough. Glucose is only partly broken down, so much less energy is released. In animals the product is lactic acid: glucose → lactic acid. In plants and yeast the products are ethanol and carbon dioxide: glucose → ethanol + carbon dioxide.
Lactic acid builds up in muscles and causes fatigue. After exercise, extra oxygen is needed to break the lactic acid down. This is called the oxygen debt, and it is why you keep breathing hard after stopping.