Einstein had two forms of his theory of relativity. The first was Special Relativity.
Special Relativity shows that there is no absolute or privileged states of rest. That is to say, there is no place (space-time) from which you can say you are at rest and all other places (reference frames) are moving. All motion is relative. Therefore, calculations of motion must be made with respect to other reference frames. Suppose you are running south at 10 miles per hour and someone is running north (towards you) at 10 miles per hour. The relative motion is 20 miles per hour between the two of you. If you are moving at different angels to each other, his motion relative to you (and vice versa) will be different. So, a third person moving in a different direction at another different angel will have different relative speed. What Special Relativity shows is the the speed of light is the samerelative to anything moving in any reference frame.
Light speed is about 186,000 miles per second. Even if you travelled 185,000 miles per second, just behind a light beam, you would not be 1,000 miles per second behind. You would be 186,000 miles per second behind because light travels at the same speed relative to all reference frames.
One of the effects of this theory was to show that, just as there are no privileged places of at-rest, there is no absolute time. As an object approaches light speed, time slows down. Therefore, time is relative to velocity. However, this is only significant for objects moving at or near the speed of light. The speed of light is the one fixed, absolute constant.
Einstein also theorized that when an object speeds up to the speed of light, since it can't go faster than this universal speed limit, any surplus energy added to make the object go faster than the speed of light will add to the object's mass since it cannot add to the object's speed. Thus, he used e=mc2 to show how this energy can be converted to mass and the process can be reversed.
General Relativity, which Einstein published about ten years after his Special theory, has to do with gravity. Since light always moves at a universal constant speed, relative to all other objects, Einstein needed to come up with a new theory of gravity in which gravity did not travel faster than light. Einstein supposed that gravity cannot travel faster than light, but yet it seemed like gravity acted on objects instantaneously. So, instead of Newton's theory of gravity where the sun reaches out and holds the planets in orbit, Einstein proposed that the sun curves space and time around itself and the planets follow those curves. Thus, he showed how space and time are an interwoven fabric because he theorized that changes in the gravitational effects (changes in the curves of space-time) would reach the objects they affect at a speed equal to that of light.
Einstein showed that time is relative (noticeable at high speeds), light speed is a constant and a universal speed limit, energy and mass are equivalent, and gravity functions by curving space-time itself.