The Special Theory of Relativity (distinguished from Galilean Relativity, a limiting case of SR or General Relativity, a generalization of SR) is based on two postulates. A postulate is a statement assumed to be true without proof. The validity of this assumption is measured by the accuracy of the consequences derived from it. There are some interesting consequences from the postulates of SR. It should be held in mind that several of these consequences were known (e.g. Lorentz transformations and the consistency of the speed of light) but had no theoretical basis. So, Einstein was, in a sense, attempting to place known experimental results on firm ground.
The first postulate is that the laws of physics are the same in all inertial reference frames. An inertial reference frame (IRF) is a frame in which Newton's First Law of motion is valid. See the discussions on Newton's Laws and centrifugal forces for an explanation of Newton's Laws. This is not an unreasonable assumption. It basically says there is no way for you to do a _local_ experiment to determine if you have a non-zero velocity. I like to think of it in the following way: You are always at rest with respect to yourself. (General relativity relaxes this from IRFs to any reference frame.)
The second postulate is that the speed of light will be the same for all observers regardless of any relative uniform motion. (It says nothing about the history of the speed of light, only that whatever that speed is it will be measured as the same speed for all observers in IRFs.) This answers the common question, if you are in a car driving at the speed of light and turn on your headlamps, what happens? The answer is the light from your lamps leave at the speed of light relative to you and relative to any external observer. This seems silly because we live our entire lives at speeds much less than the speed of light. We are used to the idea the the time elapsed between two events will be the same for all observers. This does not seem to be the case. (Galilean relativity asserts the speed of light is effectively infinite for all observers.)
The most famous consequence of these two postulates is the equivalence of mass and energy (E=mc^2). Another consequence is that no object with mass can travel at the speed of light. This is because the kinetic energy (KE), or the energy associated with the motion of the object, grows like
KE = (mv^2)/[1-(v/c)^2]^(1/2)
where m is the mass the object possesses in it's own frame, v is the speed relative to some observer in another IRF, and c is the speed of light. Since the quantity in the brackets  is in the denominator, as it shrinks the kinetic energy grows. When v = c, the bracketed term is zero and the KE is infinite. What is of note is that KE goes to infinity while v remains finite (v = c). The only way to travel at the speed of light is to have no mass, as photons do.
There is an information aspect to SR, and Einstein was very aware of this. It formed the basis of his arguments against quantum mechanics. The EPR experiment was designed to show this.