The notion called aether I am trying to learn relativity theory and going through an introductory text on special relativity. I stumbled on the Michelson-Morley experiment. The book claims (accounts) that the result of this experiments banished away the concept of Aether. In order to understand how exactly the results of this historical experiment refuted the long standing idea I think I need to know what exactly was the idea of aether. Can anyone describe the concept of aether, what were the evidences that propelled this idea? 
 A: Wikipedia is always a good place to start: Luminiferous aether.
Short answer: the aether was postulated as the medium through which light propagates. In the years prior to quantum mechanics and Relativity, Maxwell's equations very successfully characterized electromagnetic radiation as a wave, and solidified the wave nature of light among physicists.  All other "waves" with which we're familiar require a medium to travel through, (e.g. sound waves require air).  So it was a ridiculous idea to have a wave that requires no medium to travel through.
So, the Michelson-Morley experiment sought to "detect" the presence of this aether by assuming that the Earth is in motion through the aether, and measuring the speed of light at different times of the year, looking for differences in the measured speed due to the solar system's constant drift through the aether.
There wasn't really any "evidence" for the existence of the aether. It was simply assumed to exist as a necessary medium for light waves to travel through, and became entrenched in the physics of the time, until we started getting contradictory data from ever-more-precise measurement instrumentation.
A: The Michelson-Morley experiment looked for an absolutely stationary space the Earth moves through. The near-null result is evidence the aether is not an absolutely stationary space.
"The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. [..] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo." - Robert B. Laughlin, Nobel Laureate in Physics, endowed chair in physics, Stanford University
"any particle, even isolated, has to be imagined as in continuous “energetic contact” with a hidden medium ... If a hidden sub-quantum medium is assumed, knowledge of its nature would seem desirable. It certainly is of quite complex character. It could not serve as a universal reference medium, as this would be contrary to relativity theory." - Louis de Broglie, Nobel Laureate in Physics
"According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense." - Albert Einstein, Nobel Laureate in Physics
http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html
"Think of waves on the surface of water. Here we can describe two entirely different things. Either we may observe how the undulatory surface forming the boundary between water and air alters in the course of time; or else-with the help of small floats, for instance - we can observe how the position of the separate particles of water alters in the course of time. If the existence of such floats for tracking the motion of the particles of a fluid were a fundamental impossibility in physics - if, in fact nothing else whatever were observable than the shape of the space occupied by the water as it varies in time, we should have no ground for the assumption that water consists of movable particles. But all the same we could characterise it as a medium."
"More careful reflection teaches us however, that the special theory of relativity does not compel us to deny ether." - Albert Einstein
