Usually, the past lives that are recalled are mundane i.e people don't claim to be famous historical figures but rather simple folk but often in extreme situations which may explain a particular present day fear or phobia.
The possible explanations come down to five:
DELUSION : The subjects are unwittingly making up the past life. By subconsciously referencing films and books they may have forgotten, they construct a past life. It is likely that this does account for some of the examples but there are many cases where historical research proves the authenticity of the account…often revealing little known facts.
GENETIC MEMORY: This theory suggests that our memories are passed on from one generation to another through our cell structure or DNA. However some subjects are able to regress back to different cultural and racial backgrounds which a DNA based memory would preclude.
COLLECTIVE UNCONSCIOUSNESS: Accords to the work of Carl Jung, in which all men, regardless of race, religion, or background, are united by a common pool of knowledge and experience that often manifests itself in dreams.
SOUL MEMORY: This concept advances the view that we all have access to the memory of another soul, through the ‘Akashic’ records - the spiritual record of everything that has ever happened.
REINCARNATION: The belief that we return to this world many times over possibly to evolve.