From: http://www.bbc.co.uk/worldservice/learningenglish/language/2013/12/131205_todays_phrase_ask_moon.shtml

Ask for the moon

A plane passes over the face of the full moon
A plane passes over the face of the full moon as it heads for Heathrow Airport in London

Today's Phrase

To ask for the moon means to make unreasonable demands for things, or to wish for something impossible to achieve or obtain.
Examples:
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.

Take note

Don't confuse with to promise the moon (to someone), which means to make extravagant promises to someone which are difficult to deliver.
Example:
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!

Interesting fact

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.