Other forms: godlessly
Someone who doesn't believe in any god is godless. Your religious grandmother might refer to your atheist uncle as godless.
While the adjective godless literally means just "not revering a god," it's most often used by religious people or groups to criticize those who don't show the proper respect to God or religion, or those who are unbelievers. When a group is described as a "godless society," it's usually an observation of a perceived lack of morality or law, coming from the idea that people who believe in God are better, more moral citizens.