Roughly speaking, an ergodic system is one that mixes well. You get the same result whether you average its values over time or over space.
This morning I ran across the etymology of the word:
In the late 1800s, the physicist Ludwig Boltzmann needed a word to express the idea that if you took an isolated system at constant energy and let it run, any one trajectory, continued long enough, would be representative of the system as a whole. Being a highly-educated nineteenth century German-speaker, Boltzmann knew far too much ancient Greek, so he called this the “ergodic property”, from ergon “energy, work” and hodos “way, path.” The name stuck.
Found here, footnote on page 479.
More posts on ergodic systems: