The concept appears in computer security, where challenge-response authentication relies on the possession of a secret of some sort to perform authentication. A very simple example is asking for a password, where the challenge is asking for the password, and the adequate response is the correct password. More sophisticated algorithms include CRAM-MD5, or ssh's challenge-response system based on RSA [1].
The Turing test for artificial intelligence is a good example of challenge-response. A variant is Captchas, where the challenge is usually to identify letters in an image.
One real world example would be as in movies where in order to gain access to a certain location the door-man says something and the person attempting to gain access has to say the adequate response.
Many other types of challenge-response tests exist, as well.Challenge-response in computer security
Examples in other contexts