You squirrel away something when you save it for later. Lots of kids put part of their Halloween candy in a safe spot so they can eat it in a few days — in other words, they squirrel away their treats.
The phrase squirrel away clearly gets its name from the squirrel and its famous habit of storing nuts and other food for the winter. When you squirrel something away, you save it just the way a squirrel saves its acorns. You might squirrel away your lottery winnings to travel in a few years, or squirrel away the last piece of chocolate cake so that no one else in your family can eat it.