Quite often one comes across a really succinct and precise explanation of a concept. I'm wondering if it is permissible to use this explanation verbatim, if the source work is cited in your paper (next to the explanation)? What's in question here is at most 3 sentences.
No, it's not permissible. Some minor overlap in wording can occur naturally (e.g., you couldn't possibly avoid all two-word phrases anyone has ever used before), but deliberately copying text is different. If the copied text is special or remarkable and says something better than you could have said it, then you should attribute it to its source and not seem to be presenting it as your own words. Citing the source nearby is not considered enough to indicate a verbatim quote. On the other hand, if there's nothing special about the copied text, then there's no reason to copy it. (I suppose it could save you a few minutes of work in writing your own explanation to replace these sentences, but that's not considered a good excuse.)
No. It is never acceptable to use another person's exact words without quotes and a citation that includes the page number. What you are suggesting is plagiarism. If extensive quoting is not common in your field, and most people paraphrase, then I suggest you paraphrase, even if it seems that you cannot write this in any way better or even equal to what was already written.