I get this question a lot. Eve Ewing has published a guide to the “personal statement” that is brilliant and useful. She writes:
The personal statement is a slightly misleading title for this document. It is not primarily about you holistically in the way your college personal statement was. It serves ONE MAJOR PURPOSE: to demonstrate to a department that you understand how to formulate and pursue a research question, and that there is a good fit between your question and the department.
She then outlines the major elements of the statement.
Disciplines differ, but I think this is tremendously useful.