Some of these answers are tragically simplistic. They’re also kind of meta (or perhaps one of the opposites of meta), because if a question really is merely an information retrieval device then the answer to “What is a question?” is of course going to be nothing more than a straightforward regurgitation of information. Our imaginations can be useful, however.
Let’s take the polythetic entitation approach. The canonical case of a question is a person is using the [grammatical] interrogative mood to get information from another person. However, questions are an actual population of happenings in spacetime, and one by one we can relax or change the parameters of the canonical case to see how the question-population’s body is actually shaped.
1. A one-person question. Someone can ask a question not to another person, but to oneself. This can lead to introspection and a reorganization or reanalysis of already-stored sensory information (underscoring the difference between “information” and “knowledge”), or to a search for new sensory information.
2. A search for information without the interrogative mood. Someone can use the indicative mood, for instance, to get information from another person. Instead of “Did you like the outcome of the election in Brazil?” you can have “The election in Brazil was crazy!” This can obfuscate the fact that information is being sought, in order to make the askee not feel like she is being interrogated or being pushed into a debate, perhaps making her feel more free to speak her mind in any response she might produce.
3. The interrogative mood without a search for information. Someone can use the interrogative mood to surface information or a topic in a conversation without revealing that they already know the information. Instead of “I hope your children get well soon, [Person who I just met but have previously heard about and know your kids are sick]” you can have “Do you have any children, [Person who I just met but have previously heard about and know your kids are sick]?” “Yes, [Person who I have just met and literally never knew existed]” “Oh that’s nice, how are they doing?” “Oh they’ve been sick for a few days” “Oh I’m sorry, I hope they get well soon.” In this case, questions can be used to cover over the probably awkward fact that someone has heard gossip about somebody else.
4. A search for information without language. Forget grammatical moods, sometime information can be sought from other people without even language. Facial expressions, wandering hands, etc. can be used to show that one wants information and would appreciate signals in return, perhaps a pointing finger or a well-timed moan.
We can take a step back from the polythetic algorithm and meta-gaze upon this post, however. It’s ostensibly asking “What are questions?” but it might also be trying to pry open a new angle on the related discourse, or prepare its audience for a subsequent production. There’s not really enough information in this post to tell; maybe I should just ask a question.