Poor. It means the person died poor. Here is a note from Andrew Wood, the curate of Darlington St. Cuthbert, in the 1768 burial register:

"The letter P. on the margin means that the person, whose name it is set against, died poor. In a large parish like this, is is impossible for any one person to say with any certainty who died leaving effects, but one can be very sure of those who died notoriously poor. Mr. Tidy, Rector of Redmarshall, as lessee (with his brothers and sisters) of the tythes under Lord Vane, receives the mortuaries; the Court, therefore, must apply to him for what information they want in that matter."

In this context, "mortuary" means "A customary gift (usually the second best animal) paid to the parish priest from the estate of a deceased parishioner." In towns, the payment was often made from a craftsman's tool collection or an item of clothing. In 1529, a limit was set on the value of a mortuary based on the value of the estate of the deceased, and no payment was made if the estate was worth less than 10 marks (around £6). By placing "P" next to a burial, nobody would be hounding the deceased's family for death duties.

See also "What does the letter "P" mean in a baptism??