Implied powers are related to the "broad construction" that you asked about in a previous question. Implied powers are powers that are not specifically given to the government by the Constitution but which are implied (according to some) by what the Constitution does say.
Again, the major case having to do with this is McCulloch v. Maryland. In that case, the question was whether Congress had the right to create a bank. The Constitution does not give it any such right. However, the Supreme Court held that the Constitution's clause that allows Congress to provide for the "general welfare" implies that Congress can create a bank because a bank would help to provide for the general welfare.
Implied Powers of the Law reference those duties that are "obvious", not needed to be clearly written or defined in the Constitution.
Powers exercised by Congress which are not explicitly given by the constitution but necessary and proper to provide for the general welfare of its citizens.
Hamilton who argued his case against Washington, so that he could get his U.S. Bank deal approved, won with the idea of "elasticity" to the Constitution.
Interesting problem in politics, when are leaders stretch those powers so thin and our Government is trillions in debt.
Any implied, common sense, obvious, general welfare, powers tend to be an problem at some point in any situation.