The way that energy comes in is that you have a fixed (conserved) amount of it and you have to portion it out among your states. There's nothing inherently energy-related about, it just happens that we often want to look energy distributions and lots of physical systems distribute energy this way (because it's the energy distribution with maximal entropy given the constraints).

(After I wrote this I saw the sibling comment from xelxebar which is a better way of saying the same thing.)