There is some discussion on this topic in a thread here
The purpose of the pardon is to serve as a check on an overly punitive federal justice system. It originates as an extension of the right of European monarchs (in this case specifically British ones) to grant clemency or mercy to individuals guilty of crimes within their constituencies.
In the nascent United States the Chief Executive's power to pardon was strongly supported by Alexander Hamilton. As pointed out in the above thread Hamilton writes in Federalist 74 that ability to pardon will help reduce cruelty and keep the justice system merciful. He also argues that "a welltimed offer of pardon to the insurgents or rebels may restore the tranquillity of the commonwealth" The argument for good timing was a rebuttal to the proposal by Roger Sherman that the power be limited by requiring senate approval.
Its worth noting that at the time the Constitution was written the Federal Government had far fewer laws than it does today and the President only has the power to reduce sentences for federal crimes, which at the time would have consisted mostly of treason and or piracy.
Sources:
Federalist 74, retrieved here