The concept of implied powers is predominantly used in law, literature, civics, public administration, legislature, and all possible documents that empower or delegate authority. The basic meaning of the term implied power is 'authority and power that is not explicitly stated, but is rather derived as a result of situation and righteousness'.
Previously, the concept had been commonly used in judiciary and the British parliament. Alexander Hamilton was the first person to express the need of the use of this term by the Congress for the betterment and benefit of people. Simply put, implied powers are powers that are not stated, but are used for the benefit and advantage of the society, its people, and the sovereign.
What are Implied Powers?
In the modern era, the United States was one of the first nations (second only to France) to be a sovereign and republic that had a written constitution and people's rule. This basically meant that the people elected their representatives to the Congress, and a President to rule over the sovereign. The U.S. Congress and President are empowered by the U.S. Constitution to fulfill duties and use enlisted authority as and when needed, or rather, as the situation demands.
The Congress is supposed to go 'by the book', i.e., it is supposed to honor the framework of the constitution's Article 1, which commemorates its duties and authority. However, the Article 1, Section 8, and Paragraph 18 says that Congress can 'make all Laws which shall be necessary and proper for carrying into Execution the [enumerated] Powers'. This clause, which is known as the Necessary and Proper Clause, can be interpreted in two ways.
As per the clause, Thomas Jefferson furiously argued that the constitution gives the Congress the authority to take measures that are essential for implementation of powers stated in Article 1. Alexander Hamilton, however, proposed a counter argument by saying that the Congress can adopt any measure, without being subject to mention. What Jefferson meant, was that the Constitution empowers the Congress with measures that can be adopted as per Article 1, i.e., go by the book and the book only. Hamilton, however, proposed the implied powers of Congress, commenting that the framework is universal so long it remains faithful to that trust of the people. In short, use what is not written by implying it, just don't exploit it.
Among the examples of implied powers, the best one is of the 1791 National Bank charter that led to the aforementioned debate. The Constitution does not provide explicit provisos for the Congress to make a banking charter. However, based on Hamilton's thesis, the Congress passed a law to charter a national bank. Hamilton's thesis, as a common law, was tested in Supreme court in 1819 McCulloch vs. Maryland case, where the Chief Justice, John Marshall adjourned citing Hamilton's comment.
Just like the Congress, there are some essential implied powers of the President and cabinet. As a common man, even you have these powers. For example, if the legislature of your state makes some legislation that you want to protest, then you can use your right to speech and communication, and write to the people, or peacefully stage a petition or protest. Implied powers are vast, so it's a huge responsibility to have such powers. And thus, our conscience and the Constitution should be strong enough to use it properly.