a request or petition: something asked of another, whether a person in power or God, and by extension the thing that is asked for.
This is the noun that answers the common verb שָׁאַל, "to ask." Where the verb is the act of asking, this word is the ask itself: the petition a person lays before someone who can grant it. That someone is almost always a superior, a king, a powerful patron, or God, so the word carries a note of appeal rather than a casual question.
From there it slides easily to the thing being asked for. Once a petition is granted, "your request" and "what you requested" become the same object, and English works the same way: we "grant a request" and also "give someone their request." So a couple of verses lean toward the object desired rather than the appeal itself.
The book of Esther turns the word into a refrain. Again and again the king asks Esther, "What is your petition?" and pairs it with a second word (בַּקָּשָׁה) for what she is really seeking. In the story of Hannah the same word runs like a thread through the scene, since the son she is given is nothing other than the granting of her petition.