Here's a place to start;
Speed is the amount of time it takes to go a certain distance. Light's speed is always measured to be the same in every experiment, no matter which way the the observer is travelling, or at what speed. So it was concluded that, in order for light's speed to remain 670 Million mph (relative to the observer) even when the observer's speed changes (relative to whatever reference frame the observer is using), either the miles or the hours must change. So, at 669 million mph, you would still measure the speed of light to be 670 million mph, because your miles are shorter (which is called "length contraction), or your hours are longer (which is called "time dilation").
That's where all the wierdness of Relativity comes from.