There is no "implied powers clause" in the US Constitution.
What is mean by "implied powers" goes back to Alexander Hamilton. When asked by George Washington to defend a bill creating a US national bank (the First National Bank of the United States) against Thomas Jefferson's accusations that nowhere in the US Constitution was the power to create a bank (or issue money, for that matter) discussed or granted, Hamilton answered that certain powers were implied by the Constitution.
What he has been interpreted to mean is that the Constitution grants non-enumerated powers generally necessary to fulfill explicitly enumerated duties. That is, the Federal government is permitted to do things not explicitly noted, provided that such actions are reasonably required to perform a function explicitly required (or granted) by the Constitution.
The argument from Hamilton is that Implied Powers are a practical necessity, since no document would be able to explicitly name all the possible requirements for a government, and thus, without the Implied Powers, a government could not effectively function ("the constitution would be a dead letter", to quote James Madison).
In general, the "General Welfare" clause and the "necessary and proper" clause are interpreted to give the Implied Powers.
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In respect to the government and general historical development of the United States, 'implied powers' are important in several respects. In a practical way, the concept of 'implied powers' enables governmental officials and agencies to perform necessary work on behalf of the people without that work being explicitly stated or defined by constitutional documents. That such acting 'on implication' can sometimes cause conflict is undeniable; however, in such cases, the 'implied powers' become important in another respect: debated and defined by legislators and judiciaries, they provide the opportunity to clarify in yet another particular way the roles and responsibilities of government.
Implied powers
Implied powers allow the congress to have more powers because they were hinted in the consitution. Such as when they are allowed to make banks because of the power they have to manage money. It is implied that they can have a national bank.
Inherent Powers
Implied powers are what allow Congress to creatively expand its reach and power. Alexander Hamilton used the argument of implied powers to justify the creation of a national bank.
They were afraid of a tyranny.