The phrase “parchment barriers” is one that was used by James Madison in Federalist #48. He is using it to denigrate the efficacy of written guarantees of rights. He is saying that they are only parchment barriers (because of being written on parchment) that cannot really protect anyone. Therefore, he argues for the need for checks and balances.
The Constitution and the Bill of Rights, of course, provide written guarantees that the government will not be allowed to violate certain of our rights. By calling these guarantees “parchment barriers,” Madison was warning that they are not true protections. He was saying that there is not really anything in a written guarantee that will truly prevent the majority from denying rights to minorities (he was thinking of political minorities, not racial ones).
Instead, Madison said, the best way to truly protect rights is to make it harder for the government to take them away. This is why he wanted the various branches to have checks and balances over one another. He wanted a system in which it would be hard for any one branch to violate the rights of the people. This kind of barrier was a much more effective way (he thought) of protecting rights than the “parchment barriers” that purport to guarantee specific rights.