Oxford gives a nice definition: Treating serious issues with deliberately inappropriate humour. In more simple words: Making jokes "on purpose" that "should not be done in the current situation". For example: making a joke about someone's dead wife when they died recently. Or: making fun of a judge when you are in court I also want to point out that of the synonyms that Mehmet suggested, only mocking, derisive and wry are related but cannot be used in place of facetious. Cynical and ironic are completely different words.

cynical, mocking, derisive, ironic, wry, facetious