The whole special theory of relativity is mainly founded on two assumptions (postulates) that Einstein made about the nature of the universe. The first can be stated like this:
The physical laws of nature are the same in every inertial frame of reference.The only tricky part here is what we mean by "inertial frame of reference". A couple of examples may explain this. Suppose you're on an airplane, flying on a nice level trajectory, no turbulence, moving at a steady couple of hundred miles per hour. A woman across the aisle says "Toss me your bag of peanuts, will you?" You decide to oblige. (I sure wouldn't, but let's say you would.)
You grab the peanuts, then you stop to think. "I'm on an airplane that's moving at hundreds of miles per hour. Which way and how hard should I throw this bag of peanuts, so that it will actually reach this lady?"
Well, no. You don't think this at all. You just toss the bag, using the exact same throwing motion as you would if you were still at the airport waiting to taxi out to the runway. And the peanuts soar through the fetid, recycled air of the cabin in exactly the same way as if the plane were on the ground. You see, if the plane is moving at a constant speed, in a straight line, then the laws governing thrown objects are exactly the same as in a plane at rest. We call the inside of the plane an inertial frame of reference. (The word "inertial" refers ultimately to Newton's First Law of Motion. Inertia is the property every object has which causes it to either sit still or move in a straight line at a constant speed, unless there is a force acting on it. An inertial frame of reference is a frame of reference in which this condition holds.)
As another example, let's consider the ground itself. The circumference of the earth is about 40,000 kilometers. Since the earth rotates once every 24 hours, a point on the ground at the equator is actually moving eastward at a speed of over 1600 kph. And yet I'll bet Steve Young has never once worried about this fact while throwing a touchdown pass to Jerry Rice. (Feel free to imagine more current players.) That's because the ground is moving at a speed and in a direction that is approximately constant. The surface of the earth is almost an inertial reference frame, and so the fact that it's moving has very little influence on things. Everything behaves as if the ground were at rest.
Well, almost everything. There are, in fact, some phenomena that are completely inexplicable, unless we realize that the earth is rotating. (That is, the ground is not moving in a straight line, but is moving in a big circle around the earth's axis.) Many aspects of weather, for example, appear to completely violate the laws of physics, unless we account for this fact. As another example, artillery shells fired over very long distances appear not to travel in a straight line as they should in an inertial frame of reference, but to veer somewhat to the right in the northern hemisphere, or the left in the southern hemisphere. (For you golfers out there, no this does not explain your slice.) For most purposes, we can think of the earth as an inertial reference frame, but occasionally, its non-inertiality (I just made this word up, I think) has a noticeable effect.
So here's the bottom line. An inertial frame of reference is one which is either at rest or moving in a straight line at a constant speed. Einstein's first postulate is that all the laws of physics hold in such a frame. The examples of a moving airplane and the surface of the earth were just to demonstrate to you that this is a perfectly reasonable assumption that people make all the time without thinking. Who says Einstein's such a big genius?