The balloon sticks because of charge induction and charge polarization.
Work Step by Step
This is discussed on pages 416-417, and shown in Figure 22.14. The balloon becomes charged by contact and friction after being rubbed on your hair. The charged balloon induces an opposite charge on the surface of the door (i.e., it polarizes the atoms in the door). The charged balloon and the oppositely-charged door surface then attract each other.