Control authors apply this attribute to the class definition to inform template authors the types of the parts to use for styling the class. These parts are usually required in the template and have a specific predefined name. There can only be one element with a given name in any template.
For example, if you look at the class declaration of the ComboBox class, you can see that the parts PART_EditableTextBox and PART_Popup are of types TextBox and Popup respectively.
For more information, see Guidelines for Designing Stylable Controls