The reason the first national government of the United States failed under the Articles of Confederation was because the Founders, having witnessed the increasing reach of Parliament, purposely wanted to keep a confined national government with limited powers so that the balance of power would reside slightly more with each individual state, and the bulk retained by the people. Realizing that the national government was too confined, they got the balance right under the Constitution, where issues of common interests among the states were best handled -- the minting of coins to be a prime example, rather than having each state mint its own, and slow down commerce through endless currency conversions. Under the Constitution, each state ceased acting like an independent country, ceding explicit abilities to the national government. The Constitution clearly itemizes what the national government can do; (the "enumerated" powers,) the concept of "implied powers" is a fabrication. Over time, it has undermined state and local government, and made the national government unmanageable. The Founders clearly wanted a small, definable national government. Had there been a need to add to the enumerated powers, they provided for that through the process of amending the Founding Document. Sadly, politicians take the least path of resistance, and rather go through the amendment process (which to them is seen as an impediment to their grabbing power) they simply have sidestepped the issue by employing "implied" powers, where they can make the Constitution state what it does not, or worse, ignoring the Constitution altogether. Like the increasing reach of Parliament in the 1760's, the US now has the same problem with the increasing reach of its federal government.
The first answer is absolutely correct. Let me just add one thing. I want to talk about the connection between the terms "enumerated powers" and "implied powers" and federalism.
The idea of implied powers is something that helps swing the balance of federalism more towards the central government. If we believe that the elastic clause gives the federal government all these implied powers, we are giving it more power and taking the power away from the states.
So the idea of implied powers is related to federalism because it tends to give the national government more power and take power away from the states.
Federalism isn't related to this division of power - that is federalism's definition. The specific framework for the division of Federal, State and Local powers is provided for in the Constitution. For example, only the federal government can coin money or declare war, while only the states regulate drinking ages and driving laws. The 10th amendment states that any power not expressly given to the federal government in the Constitution is automatically granted to the states.
Enumerated (listed) powers are those specifically granted to the federal government in the founding document. Implied powers are when the courts and the federal government assume powers exist that they can use, even though they are not listed in the Constitution. Article I, Section 8, Clause 18 (The Elastic Clause) allows Congress to enact laws to carry out the listed powers, which can mean a great variety of things that the Framers both did and did not intend.