When we reached the point where we could demonstrate that light was a wave, then it was presumed that the wave must have a medium in which to travel. All the other waves we knew about required a medium. Since no medium was apparent between the earth and the sun, it was presumed that this medium was transparent and therefore not readily observable - it was called the "ether". The popular presumption was that this ether was stationary and filled all of space. This involved the presumption that there was an absolute reference frame in the universe, and that all the movement of planets and stars was through this ether.
These presumptions were part of the historical setting of the Michelson-Morley Experiment. With the interferometer which he invented, Michelson found no evidence of the ether, to his and everyone else's surprise. Michelson's terse description of the experiment: "The interpretation of these results is that there is no displacement of the interference bands. ... The result of the hypothesis of a stationary ether is thus shown to be incorrect." (A. A. Michelson, Am. J. Sci, 122, 120 (1881))
The proponents of an "ether" as a propagating medium for the light were not ready to give up the idea, and proposed that the Earth dragged the ether along with it in its orbit, thus accounting for the negative result of the interferometer experiment. Lord Rayleigh wrote to Michelson, urging him to repeat the experiment with greater accuracy to test these hypotheses. Repeated over the next 40 years with ever greater precision and the same negative result,this 1887 experiment is pointed to as one of the experimental foundations of relativity, and earned Michelson the Nobel Prize in 1907.
While proponents for the existence of a medium in space, an "ether", still exist, the standard position is that there is no medium in space. One of the reasons for this position is that there was no direct experimental evidence for the existence of the ether - everything can be explained without it, hence the Occam's razor approach. Another involves the preposterous mechanical properties required of a medium which supports a wave at 3 x 108 m/s. The velocity of any medium-dependent wave has the nature of the square root of an elastic property divided by an inertial or density property. To support a wave speed of the speed of light would require an incredibly high "stiffness" for space which has near zero density. A medium so tenuous that it produced no detectable drag on the planets which moved through it must yet have an incredibly high restoring force to bring it back to equilibrium once the planet passed.