To ask for the moon means to make unreasonable demands for things, or to wish for something impossible to achieve or obtain.
Bob's wife is always asking for the moon. He works hard 12 hours a day for poor pay, but she still expects expensive holidays and clothes.
Don't ask for the moon, Mr Jones. Be reasonable, please.
Don't confuse with to promise the moon (to someone), which means to make extravagant promises to someone which are difficult to deliver.
My husband promised me the moon when we got married: a big mansion, a flashy car and all the diamonds I could wear. But none of it happened!
The Apollo missions between 1969 and 1972 returned over 380kg of rocks from the moon, which have been used to help us understand its origins and structure.