The Anti-federalists, led by Thomas Jefferson and James Madison, were pushing for the addition of the Bill of Rights to the Constitution that limited government and police powers and protected free speech and gun rights. Without it, it would be difficult to get the Constitution supported by the anti-feds and ratified by enough states. George Mason in particular led opposition ot the Constitution without these written guarantees of rights, and he nearly kept Virginia from ratifying. This might have been enough by itself to defeat the Constitution's approval.
The amendment provision, and the promise by Federalists George Washington and Ben Franklin that a Bill of Rights would be supported under the new government by both sides, was enough to allow ratification to proceed. They followed through on their promise and added the first ten amendments to the Constitution in 1791 under George Washington's first administration, with a largely Federalist Congress and support from most of the states.