Eternal Return is essentially the theory that the universe follows the eternal cycle of birth and death.
(Not 100% certain on this next part of it) Each incarnation of the universe is also exact to the one that came before it, and the one that will come after it. So once this universe dies, it will be reborn, and eventually you, and I, will post on this topic talking about this theory because the new version of the universe will be exactly the same as the one we're in now, and the same events will transpire.
The universe is dying. Eventually, all solar activity will cease to exist, and the universe will lose all source of light, essentially becoming a black void. The Eternal Return concept states that when this (or a similar version of "death") happens, the Universe will be reborn once again.
This belief does have some basis in current cosmology theory. It's believed that the universe may end in a "Big Crunch" where all of the universe's matter is condensed to an infinitely small single point. This would then result in another "Big Bang" event. And the cycle would continue indefinitely.