A faculative anaerobe (or faculative bacteria) is an organism that can grow in either the presence or absence of oxygen. It does not require O2 to grow but it does tolerate its presence.
An obligate anaerobe is an organism that cannot grow in the presence of oxygen. It neither requires O2 to grow nor does it tolerate it. Obligates anaerobes do not have the necessary emzymes to rid themselves of the toxic oxygen deriviatives.