The Past Doctor (PD for short) is a mysterious Doctor who is (not informed in the episodes) The Doctor's twin future self, which means he was born in a future where The Doctors parents were still alive and that PD was born while The Doctor regenerated into his 18th self. So...basically The Doctors twin future brother who is called Past Doctor so that The Doctor does not know that he is his future twin brother. He also carries a Sonic Blaster handed down from Captain Jack Harkness to PD.