The term aether (or ether) originates from the ancient Greeks. It meant  the upper  regions of space, or the heavens; or the  substance that filled these upper regions. Some greek philosophers, most notably  Aristotle,  thought the aether to be the fifth classical element (along with water, fire, air and earth). Aristotle claimed that the heavens can't be made by any earthly substance because they are unchanging, thus they must be made of a  heavenly substance - the aether.

Later on the term was used by physicists to refer to a describe a substance, medium, or field, that fills all of space, and through which certains waves or forces can propagate. It was used to overcome apparent problems in the known theories. For example, in Newton's theory of gravity the gravitational force acts instantaneously and at a distance. This seems paradoxical, and against common sense. One solution to this problem is to introduce a medium, the gravitational aether, through which the gravitational force propagates. Now  this medium is the one to exert the force and not the actual object, so there is no more spooky action at a distance.

The most famous theory involving an aether was the luminiferous aether - the medium through which light traveled. The theory was abandoned, along with the term, in the early 20th century, when it was replaced with Einstein's theories of relativity and concepts like space-time and quantum fields.