Why does exchange energy of electrons lead to stability?

My text book says "electrons of the same spin in degenerate orbitals tend to exchange their positions and this leads to stability". Firstly, why should the electrons exchange their positions? I read somewhere that the electrons would want to exchange their positions in order to get a greater area of movement and consequently, the shielding effect by other electrons decreases. But how would exchanging of positions by electrons give them more area? Exchange of positions would basically result in the same situation as before the exchange?