A "potter's grave" is a place where people who don't have money for funeral services are buried.  It is also reserved for people who have no loved ones to bury them or people who are unidentified at their time of death.  A potter's field (where the graves are) is called so, not because it is owned by a potter, but rather because the land is barren and unable to grow crops, so it was only good for potters to dig up clay.