The Object Browser provides a list of objects in the current display that can be linked to the button whose properties you are editing; that is, when the button is pressed, the object you select will be affected.
For some buttons, there will only be type of one object in the list, because the button only works with one type of object. A Diagnostics Clear button's list, for example, will show only the Diagnostics List objects on the display, because that is the only type of object the button works with. Other buttons, such as Key buttons, will show a wider selection.