In a nutshell, you get to register your pigs as pedigree. It's the only way, unless you breed British lops or Kunekunes - both those breeds manage their own herdbooks and registrations.
Unless you want to breed pedigree pigs, or show pigs at BPA-accredited shows (only pedigree pigs allowed), there aren't many tangible benefits. You get a very basic level pig magazine (Practical Pigs) every quarter, but that's about it.