Relativity can be stated like this:
"The motions of bodies included in a given space (reference frame) are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line."
-Newton (Text in parentheses added)
This idea of relativity has been around for a long time, the statement above is from Newton's Principia. We observe this principle everyday - if I'm sitting in my car, everything inside: the seats, the steering wheel, the doors and windows all look the same when I'm sitting in the driveway and when I'm on the highway. If I'm driving at a constant speed of 100 mph, and I throw something into the backseat, like a physics book, it won't go flying through the car (i.e., the car won't 'move' beneath the book), it acts the same as if I wasn't moving.
This is accomplished mathematically using the Galilean transformations. If an observer at the side of the road sees me tossing the book into my backseat, and I give it a velocity v, then the observer would measure the book moving with my car's velocity minus its velocity, 100 - v.
Read over the Newton quote again. What this says, and what is important to Einstein's relativity, is that an observer cannot tell whether he or she is moving or at rest, simply by observing bodies in his or her own frame of reference. By observing the steering wheel or the book moving, I cannot tell if my car is in the garage or on Route 66. And actually, Route 66 is in my reference frame too, so I cannot determine if I'm moving, simply by watching the highway go by either! How do I know that I'm the one moving, and not the highway? Well, we know that we're moving and the highway isn't because we approximate the earth to possess its own inertial frame, that is, we pretend that the earth is moving with a uniform velocity and in a straight line. From this inertial frame we can determine the speeds of all moving bodies relative to that frame using the Galilean transformations. These transformations worked very well for moat observations, except when we observe the very fast.
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