Organisms that are aerobic require oxygen in order to generate ATP, whereas organisms that are anaerobic are able to generate ATP without oxygen. There are also organisms called facultative anaerobes that can do both (respiration and fermentation), examples are yeast and some bacteria. Human muscle cells can also switch over to anaerobic fermenation (called the lactic acid cycle) for ...
This solution gives a general description of the differences between anaerobic and aerobic life forms. It also discusses the evolutionary reasons for why these both exist.