What function does a breather pipe in fuel tank?

It will let air into the tank so the gas will flow better.

If you have a sealed can and try to suck out a fluid, little if any will come out. If you poke a hole in the top of the can every drop will come out. Air replaces the fluid as it comes out. Most newer cars have the pipe hooked to an "Evaporative Canister" (or Charcoal Canister) to absorb the fumes of the gas as it expands and contracts and then the "fumes" are sucked in by the intake manifold to keep the air clean.