The Federalist Papers are a collection of essays (85 in total so get comfortable) written by Alexander Hamilton, James Madison and John Jay, under the pen name 'Publius' in order to urge the ratification of the proposed Constitution. By the time the first Federalist Paper was published on October 27, 1787, the public debate was already over a month old, and the internal debate at the Constitutional Convention had begun over six months earlier.
Although addressed to the People of New York, the Federalist Papers were republished in other states and used by Federalists to persuade their respective states as well. The Federalist Papers did often need to address current particular concerns, but they followed the overall thesis stated in the first Paper.
Originally sent to amend the Articles of Confederation, the Virginia Delegation (of which Madison was a part), with the aid of like-minded delegates (including Hamilton, delegate from New York), instead proposed replacing the Articles with a new, more centralized government. Members of the smaller states feared they would be overwhelmed by the economic and political power of Virginia and New York, as well as the growing Southern and Western territories, at first refused to discuss a closer union. However, eventually the idea of a federal government- with powers given to both the states and a stronger national government- emerged. This federated form of government was not only a departure from the contemporary government, federalism itself was also a radically different philosophy and style of governance, influenced by the writings of Locke and Hobbes, as well as the still recent Revolutionary War and the events that provoked it. The written Constitution comprised of a combination of their hopes, fears, and best guesses.
(For a history of the Constitutional Convention, read the excellent books The Great Rehearsal and Miracle at Philadelphia. For an explanation of federalism as both a philosophy and a style of governance check out CGS' overview of federalism.)
Not all of the delegates accepted the proposed Constitution and several refused to sign it. These delegates led the charges against ratification.
Although collectively known as the Anti-Federalists, the detractors of the Constitution listed several different complaints. The most common fear was that the executive of the national government would develop into a monarchy, or perhaps combine with the legislature into a tyrannical aristocracy. A Bill of Rights was seen by many (including George Mason, a Convention delegate, and Patrick Henry) as the only way to protect personal rights- essential to a people who had recently fought a war for ‘life, liberty and the pursuit of happiness’, and its absence was a major obstacle to their support. Other objections included the acceptance of slavery into the Constitution- the infamous 3/5ths compromise, whereby slaves were counted towards representation in the House. This was a necessary compromise, as the southern states of South Carolina and Georgia absolutely wouldn’t have joined, but still a rather onerous one. Some felt that the size of the territory of the states would make governing impossible, and that that was the real reason for the failure of the Confederation, but that several smaller Confederacies might succeed.
The result was that not only did Hamilton (and Jay and Madison) have to prove that the Union was a viable form of government and better than the Articles, but that a change from the Articles was necessary. In order to address all of these issues, Hamilton laid out his thesis in 6 parts:
The utility of the Union to your political
prosperity
The insufficiency of the present Confederation to preserve that
Union
The necessity of a government at least equally energetic to the one
proposed, to the attainment of this object
The conformity of the proposed
Constitution to the true principles of republican government
Its analogy to
your own State constitution
and lastly
The additional security
which its adoption will afford to the preservation of that species of
government, to liberty, and to property.
The first three subjects deal with the necessity of a Union, both for survival and the attainment of liberty and are covered in the first 36 Papers. The second three discuss the merits of the proposed Constitution, and make up the remainder of the Papers (37-85