Why was the Ether Theory refused by Modern Physics? If you please explain me, I just wanted to understand it more.
It's because the luminiferous aether was, by definition, composed out of some particles or elementary building blocks with a well-defined location in space. Consequently, it picks a privileged reference frame, the rest frame of the aether. In this rest frame, the speed of light – vibrations of the aether – could be constant, $c$.
However, things moving relatively to this aether by the speed $v$ should detect a different speed of the light relatively to them – the speed would go from $c-v$ to $c+v$, depending on the direction. However, this modification of the light speed, the so-called aether wind, was shown to be non-existent by the Morley-Michelson experiment which measured the speed to be $c$ regardless of the source and the observer. This falsifies the existence of the aether.
The equivalent but even more robust refutation of the aether came from the theory. A physicist named Albert Einstein built a whole new theory of spacetime, the so-called special theory of relativity (a picture of this physicist is often being shown by the ordinary people as well), that also assumes/guarantees that the speed of light is always constant and there can't be any privileged reference frame. Relativity has been backed by the Morley-Michelson experiment as well as hundreds of much more specific experiments.
One of the things it guarantees is that light (electromagnetic radiation) has to be made out of disturbances of the empty space, the vacuum itself, and not a localized material carrier.
It's not entirely true that ether theory was refused by modern physics, but seen as superfluous and over-complicated compared to special relativity's notion of time and space. There's a version called Lorentz ether theory which postulates that it's not possible to detect the absolute ether, and gives the same results as predicted by special relativity. Hence it's not possible to experimentally determine the difference between the two theories.
But whereas LET is constructed in an hoc way by adding time dilation and Lorenz contraction into the theory to make the ether undetectable, these follow from the two postulates of SR. So the sheer elegance and simplicity in favour of SR is why it's taken more seriously than LET.
There have been many attempts over the past century to answer this question, all of them incorrect as far as I can see. The most common refutation of ether (or aether) theory is based on the null result of the Michelson-Morley experiment (about which there is no doubt, the experiment having been refined and repeated many times with the same null result). M-M could be excused for it, but there is no excuse for modern physicists making the same mistake. What everyone seems to forget is that solid matter is mostly "empty" space - the separation between atomic nuclei is about 10^5 times their diameter, as discovered by Rutherford in 1910. Also, we now know that the atoms are held in place by electromagetic fields, so that the lengths of the arms of M-M's interferometer would be subject to the same effects of different light (e-m field) speeds as the interfering light beams themselves. This ("Lorentz contraction") is not an ad hoc effect, but follows from the finite speed of field changes within solids, limited to the same speed as the light beams bouncing to and fro among the interferometer mirrors.
This physical explanation for Lorentz contraction is set out well by Feynman in his Lectures on Physics, Vol II, Sec. 21-6 on retarded potential effects. The only physical constraint needed to explain relativistic length and clock/time effects in Lorentz Ether Theory (LET) is that light is the fastest signal in empty space. In practice, the ether as a unique reference frame for e-m field (e.g. light) propagation can be ignored because the experimental predictions of LET are always identical with those of Special Relativity (SR). But whereas SR offers no physical explanation for relativity beyond asserting the principle, LET does, which should surely be more satisfactory for physicists! Any inertial observer can assume that the speed of light is the same in all directions around him/her, but so can any other inertial observer, and they can not all be right, as is shown by the fact that they will disagree about estimates of the timing of simultaneous events, for example! LET shows exactly how this works in terms of the speed of light as an upper limit, as was known by Poincare in his 1904 St Louis World's Fair lecture "Science et Hypothese", in which he speculated about the collapse of relativity as a universal principle if anything can go faster than light.
By about 1920, Einstein had realised his error in declaring the ether superfluous as a concept, because he had realised that a unique, universal reference frame is implied by General Relativity in which the speed of light becomes locally dependent on gravitational potential around masses, instead of being absolutely fixed in value everywhere as in SR and LET. But noone seems to have been ready for that backflip. Instead, conceptual nonsenses like "curved space" are now preferred to a straighforward dependence of light speed on position in a gravitational field!
In summary, LET = SR in all predictions, but in my view LET is superior because it contains a physical explanation (light speed in a unique inertial reference frame as an upper limit), rather than relying on a statement of a principle - how do atoms know about principles?
The next interesting question is how does "empty space" (or "ether", to give a name for the concept of a space with physical properties) control the speed of light, between and inside atoms, and as slowed down near large masses? Does Higgs Boson theory shed any light on this (sorry!)?
(See trevm42 on Youtube)
There are a number of experiments that disproved that there exists an inertial frame against which everything is moving, and electromagnetic waves propagate, the luminiferous aether. There exists a wikipedia article that covers these questions.
There never was really any experimental or observation evidence that the luminous aether ever existed in the first place. It was merely an invention to pave over a gap in the Newtonian model of light.
Up until the mid-19th century everyone thought that Newton's experiments with prisms and slits had conclusively demonstrated that light was a wave phenomena i.e. it behaved just like waves in water. That, however, raised the question of "waves in what?" The answer was the "aether", something that couldn't be seen, touched or measured but whose motion transmitted light just like the motion of water transmitted the force of a wave.
Basically, the luminous aether was just a concept that the era's scientist pulled out of their collective… er, hats.
By contrast, Leibniz argued, purely on philosophical grounds, that light must be made of particles. Leibniz lost the argument because his hypothesis didn't have the experimental predictive power that Newton's did. However, if Leibniz's idea had been the dominate idea, the concept of luminous aether would have never been invented in the first place.
Prior to the late-19th century the idea of "subtle fluids" was evoked to explain many phenomena such as heat and electricity. That is why even today we talk of electricity "flowing" in "currents."
The history of science is filled with such inventions that paper over gaps in existing knowledge.