Jessica's family brought her to St. Catherine's school, where the narrator goes, so that Jessica could receive treatments from her burns at a nearby hospital (in New Haven).
In Chapter 6, when Mrs. Tracy is preparing Tom and his classmates for Jessica's entrance, she mentions that information about the hospital as she's warning the students to behave "as good children should" when they meet Jessica and see how her burned skin makes her look very unusual.
In Chapter 8, we get a few more details about the reason for Jessica's arrival, as Tom overhears how Jessica's family moved down from Boston, and that they were renting a condo. (The fact that the family is renting a home, and not purchasing one, is a little clue showing us that Jessica may not stay for very long and may soon be out of the narrator's life.) We also find out then that Jessica's condo is near Tom's house; we know then that they might interact outside of school, since they live so close together.