The Federalist Papers are a group of articles, 85 of them, that appeared in the New York City newspapers from October 1787 and August 1788. 51 of the articles were written by Alexander Hamilton, 29 by James Madison and five by John Jay all under the pseudonym Publius. The purpose of these articles were to convince people to ratify the US Constitution. It was written in response to the Anti-Federalist papers that appeared in the same papers earlier in 1787.
The most important issues addressed by The Federalist Papers was the role of the president. At the time, the idea that the US should have three presidents was common to avoid the presidency from evolving into a monarchy. The Federalist Papers argued for one president with limited power. One of the most controversial power of the presidency was his ability to declare war. Among other things, the papers addressed judicial review and the fact that the Constitution was a flawed document. Because it was flawed, it was suggested that it be revisited every 20 years with another Constitutional Convention. The next time you hear someone mention the original intent of the Constitution, you might want to mention this.
The Federalists obviously won this battle but much of the Anti-Federalist's concerns were addressed in the Bill of Rights published a few years later.