The payment system is the set of institutional arrangements through which purchasing power is transferred from one transactor in exchange to another.
This "exchange" is very necessary for achieving specialization in production (See A.2.1). Again, for efficient exchange, a common medium of exchange or means of payment is required. Such common medium of exchange is what we call money.
Thus the payment system (like monetary system) is also organized around the use of money.
An efficient organization of monetary system is the sine qua non of an efficient payment system. An efficient payment system should permit all kinds of payment (small, large, local, out of the town, foreign etc.) to be made with utmost speed, safely and less cost.