Nominal money, in economics, is the quantity of money measured in a particular currency, and is directly proportional to the price level. Economics (deriving from the Greek words οίκω [oeko], house, and νέμω [nemo], distribute) is the social science that studies the allocation of scarce resources through measurable variables. ...

This means, among other things, that if the price level rises by 10%, people hold 10% more money than before. (ceteris paribus)

For example, if you hold $20 to buy pizza, and the price level increases by 10%, you essentially increase your money holding by $2, totaling $22.

Real money is the quantity of money measured as a constant (eg: the value of the dollar in 1997), and relates to the above as follows:

Nominal money = Price level * Real money.

Hence Real Money = Nominal money/Price Level, and is the quantity of money measured in terms of what it will buy.

Thus, your $22 at the new price level will buy you the same amount of goods and is the same quantity of real money as your $20 at the original price level.