Obligate anaerobes are micro organisms killed by normal atmospheric concentrations of oxygen (ie,20.95% O2) By contrast, an obligate anaerobe is an organism which cannot survive in an highly oxygenated environment.
A facultative anaerobe is, simply speaking, an organism which possesses the ability to survive in an environment containing oxygen while growing even more efficiently in an environment without oxygen.
Facultative anaerobes can optionally function without oxygen by fermentation.