Sean Carroll in Cosmic Variance:
Back in the later years of the 19th century, physicists had put together an incredibly successful synthesis of electricity and magnetism, topped by the work of James Clerk Maxwell. They had managed to show that these two apparently distinct phenomena were different manifestations of a single underlying “electromagnetism.” One of Maxwell’s personal triumphs was to show that this new theory implied the existence of waves traveling at the speed of light — indeed, these waves arelight, not to mention radio waves and X-rays and the rest of the electromagnetic radiation spectrum.
The puzzle was that waves were supposed to represent oscillations in some underlying substance, like water waves on an ocean. If light was an electromagnetic wave, what was “waving”? The proposed answer was the aether, sometimes called the “luminiferous aether” to distinguish it from the classical element. This idea had a direct implication: that Maxwell’s description of electromagnetism would be appropriate as long as we were at rest with respect to the aether, but that its predictions (for the speed of light, for example) would change as we moved through the aether. The hunt was to find experimental evidence for this idea, but attempts came up short. TheMichelson-Morley experiment, in particular, implied that the speed of light did not change as the Earth moved through space, in apparent contradiction with the aether idea.
So the aether was a theoretical idea that never found experimental support. In 1905 Einstein pointed out how to preserve the symmetries of Maxwell’s equations without referring to aether at all, in the special theory of relativity, and the idea was relegated to the trash bin of scientific history.
More here.