The main points of Federalist No. 51 outline the system of checks and balances put in place to ensure no one branch of the U.S. government becomes more powerful than another. According to the Bill of Rights Institute, the 51st of the Federalist Papers explains and defends the system of checks and balances put into the Constitution that prevent both the government and factions from having too much control.
Federalist No. 51, written anonymously by James Madison, has a number of main points; the biggest idea it defends is the way in which the Constitution sets up the government. To ensure protection against tyranny or a single all-powerful branch, it is necessary to ensure that each branch is as independent and secure as the others. In Federalist No. 51, as quoted at Constitution.org, Madison explains that "the great security against a gradual concentration of the several powers in the same department" is dependent upon their ability to stay independent and stop the other branches from encroaching on them.
Wikipedia explains Madison's other main point being that the republican government proposed in the Constitution provides a check on both the power of factions and the tyranny of the majority. According to Federalist No. 51, the goal of the government is to protect rights of the people. The Constitution is the best way to ensure that no part of the government, and no part of society, can get too much control over the others.