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.
There are many ways to write this document, but its function, as Ewing says, is the aspect to keep in mind and the piece that’s often most mysterious to undergrads.
Disciplines differ, but I think this is tremendously useful.