Here is how I explained my little sister what money is:
Imagine we live in a world without money. You need someone to clean your house today and I am your neighbour who would be happy to do it. You promise me a basket of apples in the autumn for doing you this favour. Then one month later I meet someone who makes carpets and I realize I need the carpet more than the apples. I tell him to go to the apple guy in the autumn with a note from me where I say he can give the carpet guy the apples he owes me.
This note I made so that the carpet guy can collect my apples is basically money. And in this respect is a way to keep track who owes something to whom. The genius thing about money as we know it today is that it takes out the "who" part from the picture. As long as we all believe in it as a measure of value owed it doesn't matter where it came from and who owes it to whom. You give value to someone and then you can buy value from anyone.
Note I said "value owed" and not just "value" because it doesn't stand as an universal measure of value, it is a relative one. When we say money is a measure of value owed, we can just as well say it is a measure of debt. When you give more value than what you consume, you become richer, and the more others value what you do for them, the richer you become.