The main purpose of federalist was

Although the primary purpose of The Federalist was to convince New Yorkers to send to the Constitutional Convention delegates who would vote to ratify the Constitution, fully two-thirds of New York's delegates initially opposed ratification ...

The main purpose of The Federalist Papers was to explain the newly proposed constitution (we had a first constitution called The Articles of Confederation) to the people of New York in the hopes of encouraging them to ratify the new constitution in the upcoming ratifying convention