They referred to a substance thought in ancient times to fill the upper regions of space, beyond the clouds. In mythology, it referred to the 'pure' air that the Gods breathed, as opposed to the impure air that we humans breath.
Aristotle actually included it as a fifth element, together with the four others: Fire, Earth, Air, Water, working on the principle that a vacuum did in fact, not exist.
The ancients believed it to be the substance which filled all of space. More recent people such as James Clerk Maxwell, Lord Kelvin, and Nikola Tesla, held a view that the aether was more akin to being the electromagnetic field of the universe.
No matter how we try and explain the phenomenon, we never seem to come up with an answer satisfactory to everyone. Modern physics does its best to debunk the possibility of Aether, even though Einstein included it with his relativity theory.
Unfortunately, as our understanding of the ancient knowledge and philosophies grows, modern science seems to fail us more and more. (Aetheric Connections)