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There have been a few questions of the form "What is this mathematical concept?" On MO, there were several at the beginning, including some asked by reputed mathematicians, but since then they've been discouraged.

My question is what the community thinks should be acceptable here. On the one hand, it's a reasonable enough question to ask, and I don't believe we want to be as nitpicky with questions (at least, not at the beginning). On the other hand, it would be nice to know what others have already done to understand the definition, and some motivation for the question.

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  • $\begingroup$ Could you link the examples you've seen? It's possible there are some that would be acceptable and some not. $\endgroup$ – Nick Jul 22 '10 at 22:06
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    $\begingroup$ I, for one, (in the case that they are unmotivated) will vote to close these as soon as possible and vote them down. $\endgroup$ – 97832123 Jul 22 '10 at 22:29
  • $\begingroup$ I would leave a comment asking for an edit that makes clearer the level and slant a useful answer would be pitched at, and vote to close soon after if the asker seems unable or unwilling to make such an edit promptly. I think we should have an FAQ answer on "What is X?" questions, both answering them well and why they might be closed, and if we did have such an FAQ I mimght refer the asker there. $\endgroup$ – Jamie Banks Jul 23 '10 at 2:17
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For my money they're way on topic- sometimes wikipedia et al. just don't cut it for informal, direct explanations.

As for the unmotivated ones with no background, I'd wager the voting system would see to that: if your question is properly motivated and with decent background, those with less experience would be intrigued enough to upvote and those with more would recognise it as a good question and upvote it for that reason. A section in the FAQ about asking/voting on questions of this type would, I think, seal the deal.

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I think that questions titled "what is X?" is a broad enough category that they deserve a treatment similar to that of homework questions: the goal should not be to establish whether they should be allowed or not, but rather to agree on how they can be asked in an acceptable manner.

If a question is something small and simple, with a definite answer, like "what does this symbol mean?" I see no harm in answering it. The one previously asked received helpful, informative answers, and now anyone with the same question will be able to find it with a search without wading through pages of porn.

If a question is somewhat open-ended, but the asker gives enough background and details to establish exactly what he/she is looking for, that's also fine. If such details are missing, ask for them in a comment. When they get added, answer the question. This question on well-behaved functions is an example of that process working successfully.
This question on limits is missing that last step. As a result, it's not really clear what a good or correct answer would be. I will try to write my own comprehensive answer to the question this weekend, aimed at a typical college freshman, simply because I think it is important to have such an answer on this site to be pointed to in the future. Even so, I have no way of knowing whether I am really giving the question answerer what he is looking for.
In fact, I might be in favor of allowing these types of questions for such fundamental concepts like 'limits' or 'proofs' in the beginning, so that in the future, there will be an annotated list of high-quality answers that can be used as a reference.

A question that is clearly a joke or is impossible to answer deserves to be closed promptly.

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I think these questions are good, as long as nobody just starts going through a mathematical dictionary and spamming to gain reputation.

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