The amount of wealth that households and business desire to hold in the form of money balances is called the 'demand for money'.
Individuals and firms have at their command only limited resources in the form of current income and total accumulated assets. They must make choices concerning their allocation and must constantly balance the advantage of holding more of one asset against the disadvantage of holding less of others. The theory of demand for money is one part of the theory of choice in the allocation of these resources.
Why do individuals and businesses hold money? Usually, money held yields no explicit income and by holding money instead of devoting it to some other uses one forgoes income. But, the fact that people do hold money balances suggests that holding money must yield some sort of advantage or provide some sort of service to the individual.
In all these theories, narrow definition of money (i.e. coins, paper money and demand deposits at commercial banks) is preferred and it is assumed that money yields no interest return.