Updated: Jun 4, 2021
Imagine you're iron man and you're traversing through air by flying (also it's at night). You're also moving with a definite velocity without a change in your direction. Now, there are two 747's on your path having the same velocity but are in opposite directions to each other. Since, the given description is at night, it is obvious that both the jet have their strobe lights turned on. Now, considering you as a rigid reference body you find that the light from both the jets doesn't reach you simultaneously, whereas, when i look up at the sky i find that the light from both the jets reaches you simultaneously (considering i am observing the event from a roof top at rest with regards to my co-ordinates).
Consider, another instance and this is one of my favorite examples, its by Brain Greene from his book 'The elegant universe'. Picture that there are two nations that have long been at war. They are called forward and backward land. Now, the two nations have finally come to a peace treaty, but neither presidents of these countries wants to sign the treaty before the other. So, they need some scheme that they will each sign the treaty simultaneously. They consult the UN and come up with a plan. The two presidents will be seated at the opposite end of a long train and a bulb will be placed between them and the bulb will initially be in the off position. And then the secretary general will turn on the bulb, sending light heading left and right and since the speed of light is constant, it isn't effected by the direction in which it moves, also both presidents are equidistant from the bulb. So,the travel time of light to each presidents eye ball will be the same, when they see the light each president picks up the pen and signs the treaty. And what they add to the process is that the general says, when you sign the treaty let the inhabitants of the two nations that live on the opposite sides of a railroad track, let them watch the signing ceremony. As the train could go right along that track and both presidents agree to the idea, so that both parties could witness this historic moment. On the day of the ceremony, the two presidents are seated in the train, with the president of forward land facing forward and the president of the backward land facing backward. And when the train approaches the station where the inhabitants of both the nations are present, the general decides to turn the bulbs on. As he does so, the light reaches the two presidents on-board the train simultaneous with regards to the general and the two presidents sign the treaty. But, later the news arrives that a riot has broken out at the station, and the reason behind it is that the light did not reach the two presidents simultaneously. The light reached the president of the backward land first with regard to the people on the platform.
The other example would be the one Einstein initially gave, visualizing a particular body of reference, like a railway embankment. Considering, a very long train traveling along the rails with a constant velocity and in the same direction. People on-board the train will consider the train itself as a rigid reference-body, they regard all the events in reference to the train. Now contemplate a lightning has struck the railway embankment at two places far distant from each other. Now, obviously the main question that arises is whether the two events, i.e., the lightning strikes, are they simultaneous with reference to the the railway embankment and also simultaneous relatively to the train?
And the answer to that would be that the two lightning strokes are simultaneous with respect to the embankment, and the people would find that the two strikes occur at the same time. But, for a person on-board the train which moving in the direction of one of the strikes, would find that the two lightning strikes aren't simultaneous. He/she would find that the lightning strike toward which they are traveling will occur first.
The three examples tells us that the events that seems to be simultaneous in view of one frame of reference is not the same in any other frame of reference, that is relativity of simultaneity. Every co-ordinate system has its own time, Further we know the rigid reference body to which the statement of time refers, then there is no sense in a statement of the time of an occurrence. In the three examples its evident that the light reached first to the reference body that was traveling in the direction of one of the sources in a lower period of time, as a consequence the two sources of light doesn't seem simultaneous to that reference body. This itself disregards the fact, which was known before the theory of relativity, that time is independent of the state of motion of the body of a reference. It gave time a completely different perception, time is more like the progression of events with regard to a particular reference or co-ordinates, which can change from place to place. Everyone of us have a different perspective of time, we all have our own time.