Anaerobic respiration is any type of respiration which does not need oxygen.
When we are exercising hard, we may be unable to supply our muscles with enough oxygen for aerobic respiration (we just can't breathe enough air to get the quantities required into the bloodstream).
In this case, muscle cells can use a different set of chemical reactions to break down glucose and release energy, one that does not require oxygen, ie they use anaerobic respiration.
This form of anaerobic respiration is called lactic acid fermentation, as its main by-product is lactic acid.
Other forms of anaerobic respiration exist - for example, some bacteria in the soil, where there is little or no oxygen present, break down nitrates to release energy.