According to ancient wisdom the world and the heavens were composed of the four elements Earth, Water, Air, Fire and, a fifth element, Aether. Each had its natural place with Earth being the lowest and densest element and the other ranking successively above it with Aether, the lightest and quickest, being above all else*. The Aether was presumed to be what remained when all the other elements were removed in lieu of a Void. Position was achieved through displacement which explained why Fire rose and Earth fell. A substance could have varying proportions of these elements. Aether provided the medium through which light traveled as sound does through the air.
If an aether actually exists its nature must be more complex than that of the air which consists of finely divided particles. Air tends to fill all the space that is available to it. The collisions between particles allows sound to travel from one place to another.
Is the same true for aether and light? There are aether theories that have been proposed to explain the propagation of light. But the analogy of light and sound is not a good one since the properties of light differ from those of sound. Sound which travels through solid matter and air by collisions is a longitudinal wave in which compression and rarefaction take place along the path of travel. Light is a transverse wave and the changes take place normal to the direction of travel. As a result light can be polarized in two directions perpendicular to each other. So if light were carried by some sort of fluid, its aether would have properties different than that of air.
Both electric and magnetic fields can exist in a vacuum so their force fields might be considered properties of a hypothetical aether. But all that we know about electromagnetism are the forces that result from the fields. Maxwell's equations tell us how these fields change in position and time but electromagnetism takes these fields as its foundation in much the same way that Lambert took the intensity of light as his starting point. We don't need to talk about the properties of an aether. Maxwell was able to show that his equations predicted waves which traveled at the speed of light.
The null result of the Michelson-Morley experiment did not immediately do away with the aether. Lorentz was able to reconcile matters with an aether theory by postulating time dilatation and length contraction. But it was gradually realized that reference to an aether was not necessary and the result was Relativity.
For a more thorough discussion of the history involved see:
Maxwell on the Electromagnetic Field, Simpson
A History of the Theories of Aether & Electricity, Whittaker
*Supplemental (Mar 5): How could one justify this hierarchy? Presumably, you have to be quick to stay on top. It's the natural order of things.