Special relativity is one of the core concepts of relativity.
Michelson Morley Experiment
A key component of classical physics was the existence of the all pervading ether. According to this concept, the speed of light should have changed with the rotation of the earth in ether - light moving in the direction of motion of earth should have moved slower with respect to the earth than light moving in the opposite direction, as everything had an absolute speed relative to ether. Classical physicists believed this, but nobody had been able to prove it.
In 1887, Albert Michelson and Edward Morley designed the most famous experiment ever to prove this and put it beyond doubt.
As the legend goes, they failed and created history.
The Principle of Relativity
This is the most fundamental theorem of physics. According to it, there is nothing called absolute uniform motion. All motion is relative. We all know that (if we consider the motion of a train to be uniform) the landscape seems to be moving by someone in the train, and the train seems to be moving by to someone outside. The Principle of Relativity says it is impossible to ascertain that one of them is correct while the other is wrong.
The Speed of Light Postulate
The speed of light is the same for all people - regardless of their relative uniform velocities. This was something that was proved by Michelson and Morley, but can also be gathered from a simple thought experiment.
Suppose you are sitting in a vessel that is moving at the speed of light. If the speed of light is not constant, it should be zero relative to you. Then if you look back, the part behind you should be dark, as it is impossible for the light from there to reach you. So you can ascertain that you are moving, which is a violation of the Principle of Relativity.
In the beginning of the 20th century Albert Einstein was working as a clerk in the Swiss patent office of Bern. He is said to have had a brainwave in 1905, which led to the birth of special relativity. Though nowhere near as revolutionary as General Relativity, it was quite enough to make Einstein famous in the world of physics.
Relativity of Simultaneity
Simultaneity is not absolute. If two events seem simultaneous to A, they will not seems simultaneous to B if B is moving relative to A. This effect is appreciable if their relative velocity is near the speed of light.
Relativity of Time
Time is not absolute either. The time interval between two events will be different for two people moving relative to themselves. This difference is significant only if their relative velocity is near the speed of light.
Relativity of Length
Finally, length is not absolute. The length of a moving train will be different for two people if one is standing on the train while the other is outside on the ground (in fact, any relative motion between them will suffice). As you may have guessed, this difference is noticeable only if the speed of the train (which is the relative velocity between them) is near the speed of light.