The Michelson-Morley experiment was an important physics experiment performed in 1887 by Albert Michelson and Edward Morley. The experiment attempted to measure the motion of the earth through the aether and failed to do so. This unexpected failure lead to the Theory of relativity.
The experiment was performed in the days when technology had just become sufficiently advanced to accurately measure the speed of light. At that time it was known that light behaved like a wave. Scientists believed that light waves (consisting of photons) traveled through a medium referred to as the aether (sometimes spelled ether). The aether was believed to be fixed in space and so was regarded as an absolute frame of reference, relative to which the velocity of any object could (in theory), be measured. The concept of the eather was in some ways similar to the modern concept of "space-time" though some differences exist. Thus the idea was that absolute movement existed.
Scientists at the time thought that if they could accurately measure the relative velocity between the earth and light waves, they might get different results for the speed of the light waves moving in different directions. They believed this would happen because the earth was constantly moving, and the aether was fixed. By examining the results they could measure the relative velocity between the earth and the aether, and hence determine the absolute velocity of the earth through space. The Michelson-Morley experiment was an attempt to do that.
Results of the Experiment
The experiment gave unexpected results. The speed of light was found to be the same regardless of the direction the light was traveling in. At first it was assumed that the result was due to poor equipment or some other anomaly, but further work ruled that possibility out.
Consequences of the results
Scientists then faced the dilemma. They believed the earth was moving through space, but the Michelson-Morley experiment and similar experiments indicated that the earth was somehow stationery relative to the aether at all times.
A number of theories were proposed to explain the paradox, including the idea that the aether might in some way be "dragged along" by the earth. In the end the theory of special relativity became the accepted explanation, and the aether appeared to be unobservable.