A mainspring pushes hard when full and weakly when nearly spent, and the balance can feel the difference. A remontoir d’egalite is a small secondary spring between the train and the escapement, rewound automatically every few seconds — so the escapement only ever feels the small spring, freshly wound, forever.
It is complicated, delicate, and arguably unnecessary in a modern movement. We build it anyway, in every RM-03. The name is a commitment to that kind of decision.