For those people who are finding it difficult to understand the behavior of the actual Michaelson-Morely apparatus, allow me to offer this layman's analogy.
Recall that the Michaelson-Morely experiment was designed to detect the motion of the earth through something called the Luminiferous Aether.
Toward the end of the 19th and beginning of the 20th centuries, a theory was coming into acceptance that light was a wave. The existence of the luminiferous aether was a requirement of that theory because all waves need a medium through which to propagate. And outer space, through which light passed to get to us from the distant stars and through which earth itself moved, seemed to be empty. So physicists were driven to the conclusion that outer space was not empty. Earth, all the planets and stars were actually moving through a medium which they labeled the luminiferous aether. And it was this medium that supported the propagation of light waves. Unfortunately, the existence of the luminiferous aether created more problems than it solved. It had to be invisible and weightless. The stars and planets had to experience no drag as they moved through it. In fact, any attempt to measure any physical property of the luminiferous aether came up blank. In physics, if something doesn't have any measurable physical properties, if it doesn't interact with anything else, then you are not really justified in claiming it exists.
The Michaelson-Morely experiment was intended to resolve this conundrum. It used a recent invention called an interferometer which, when properly set up, could produce interference patterns by splitting and then rejoining a stream of light from a single source. The fact that an interferometer could do that was considered one of the "proofs" that light was a wave. Getting an inteference pattern in an interferometer at that time was no easy task. It required painstaking setup. And once set up, the slightest change to the apparatus or the environment around it could destroy the pattern.
This is a good place to explain what is required for two streams of light waves to create an interference pattern. The two streams must have the following characteristics:
All the waves in both streams must have reasonably close to the same wavelength.
2. Same speed:
All the waves in both streams must have reasonably close to the same speed.
All the waves in both streams must be oscillating in reasonably close to the same plane.
The crests of both streams must consistently coincide at the detection surface, as also the troughs.
Another important point to keep in mind is that the experiment did not involve any actual measurements. This may come as a surprise to many since presentations of the experiment are always accompanied by some geometry equations. Those equations provide the reader with an explanation of why you expect an interference pattern. But think about it. To use those equations to evaluate the results of the experiment, you would have to measure the path length of the light streams to an accuracy of nano-meters. And to calculate light speed you would have to measure the arrival of the light at the interference screen to an accuracy of nano-seconds. That kind of accuracy is difficult to get today never mind in Mr. Michaelson's era.
Yet Michaelson still thought he could use an interferometer to demonstrate movement through the luminiferous aether. His argument went something like this. If the luminiferous aether exists and the interferometer is moving through it, the speed and direction of the interferometer through the luminiferous aether could be made to enhance or cancel the interference pattern. Michaelson designed an interferometer which, when set up, only worked for one specific alignment as it moved through the luminiferous aether. Then, after the interferometer was set up and the interference pattern had been recorded, he intended to rotate the apparatus. If the inteferometer was not moving through the luminiferous aether (or if the aether did not exist) the rotation would not make a difference. But since the surface of the earth was rotating and the earth itself was orbiting the sun, the chances of the inteferometer being at rest with respect to the luminiferous aether was considered impossible. Also, even though the apparatus was designed to be rotated, the constant movement of the Earth meant Michaelson didn't have to do the rotating himself, if he was willing to wait a few hours. Regardless of how the apparatus was rotated, after rotation Michaelson expected the interference pattern to disappear.
The fact that the interference pattern did not disappear was a surprising and serious challenge to the wave theory of light. Historical accounts indicate Michaelson considered his experiment and the apparatus he built to be a failure. Little did he realize it would become one of the pillars of modern physics.
Say Mr. Michaelson is standing in the fog on the edge of a body of water and wants to find out if there is a current in it. He can't just throw something in the water and watch. We need to assume he can't see it. He has two identical boats. He also has two long poles not necessarily the same length. The important part of this analogy is that he doesn't have the ability to measure or match the lengths of the poles. He also doesn't have an accurate clock.
Here is how he decides if there is a current. He lays one pole at the water's edge parallel to the bank. He instructs Mr. Morely to drive one boat from one end of the pole to the other and back. He suspends the other pole over the water perpendicular to the first making two sides of a right triangle. He drives the second boat himself from one end of that pole to the other and back. Now if both boats start together and both poles are the same length and there is no current, he expects both boats to arrive back together. If there is a current, the boat traveling parallel to the shore will gain some time during one leg of the trip but loose the same time during the other leg. So its trip will take the same time as if there were no current. Not so for the boat traveling crosscurrent. It will get dragged down stream by any current and will have a slightly longer trip. That will take longer and the boats not will arrive back together.
But the poles are not the same length so the odds of the boats arriving back together, current or no current, are pretty much zero. What to do. Mr. Michaelson asks Mr. Moreley to be patient and keep re-running the experiment. With each run, Mr. Michaelson cuts a small amount off the pole whose boat took longer to get back until he gets a run in which both boats arrive back at the same time. This means he has one of two scenarios. There could be no current and both poles are now the same length. Or, there could be a current but the poles are now of such different lengths as to compensate for the effect of that current.
Now what? Here is the brilliance in the experiment. Mr. Michaelson switches poles. Now, if there is no current and the poles are the same length, switching them will not make any difference. The boats will arrive back together again. But if there is a current and the poles are not the same length, switching them will screw up the compensation. The boats will not arrive back together. Mr. Michaelson has a method of determining if there is a current without the use of clocks and without the use of a measuring tape.
The Michaelson-Morely experiment was conducted wholly within the same room. The source of the light was a sodium-vapor flame at rest with respect to the interferometer that was analyzing it. The experiment was not designed to reveal any information about light emitted from an object moving with respect to an observer (although one can make certain inferences). The experiment was designed to reveal the presence of ether drag and nothing else. It failed to reveal that drag.