It comes in many varieties, and many forms. Fundamentally it is rust (or to be more precise iron III oxide), often suspended in wax or other soft medium, or simply in graded powder from. It has been used for centuries to polish precious metals as it is a relatively soft abrasive.
The term "jewelers rouge" is also sometimes used in a more generic form, to indicate any form of jewelers polishing compound, so I've seen people referring to "green rouge" polishing compound etc.
A good watch cleaning machine will clean all parts of the watch including pivots and the holes in which they fit. If a pivot is worn the wheel should be replaced, if a replacement can’t be found, then the pivot should be repaired, ending with burnishing.