It means that the organism does not require air (oxygen) to live.
Anaerobic organisms are organisms that cannot live in the presence of air. Anaerobic organisms are found in anoxic environments (one which lacks oxygen). The two types of anaerobes are facultative and obligate anaerobes. The facultative anaerobes (such as Staphylococcus aureus) can live with or without oxygen while obligate anaerobes (such as Clostridium tetani) must live without oxygen.