An enigma is a puzzle, or something mysterious and difficult to explain. People often use the term to imply that the puzzle or problem is intellectual in nature, requiring the full force of someone's deductive ability to solve it. The term was borrowed as a name for a coding machine used in the Second World War; the Enigma machine relied on a complex series of steps and devices to make virtually unbreakable codes. The only way to solve the Enigma was to steal a machine and its codebook, since the codes it generated were so complex.

The term is derived from the Greek ainig, which means “to speak in riddles.” Enigmas can take a wide range of forms, including puzzles, riddles, mysteries, secrets, ambiguities, conundrums, perplexities, and things which are simply inexplicable. Enigmas may also combine these elements, as Winston Churchill famously noted when he said that “Russia is a riddle wrapped inside a mystery inside an enigma.”

Because humans have a natural sense of curiosity, an enigma is often a topic of intense interest, discussion, and debate before it is solved. Some famous historical enigmas have captivated the imagination of some of the greatest minds in the world, and continue to do so, as is the case with Fermat's last theorem in mathematics. Some people relish the intellectual challenge of an enigma, as it allows them to prove their intellectual capabilities to themselves and others.

Some employers use enigmas in interviews or employment testing to determine whether employees are a good fit with them. These puzzles may relate to the field the company works in, as might be the case with a software company which challenges applicants to find the flaw in a presented piece of code, or they might just be general intellectual challenges. The successful completion of an enigma can indicate that an employee will be able to think creatively to solve problems, and the process which the applicant goes through to solve the problem can also be of interest to potential employers.

Someone who speaks in riddles may be called “enigmatic.” Many examples of enigmatic individuals can be found in history and in literature; such individuals are sometimes treated as great minds, since it is assumed that their brains simply work too quickly to allow normal individuals to comprehend them.