Okay, well, lets look at this for second in the way Einstein did more than a century ago. You are sitting at your computer and you have a flash light. You point the flash light in some direction and measure the speed of the light in the beam. And no surprise, you find that the light is moving at the
speed of light.
But then you ask yourself the hard question... while it seems like you are not moving, you are on the Earth, which is spinning and orbiting the Sun, and the Sun is orbiting the Milky Way... you quickly realize that you are very far from sitting still. In all actuality, you are moving at a very high rate of speed.
But then you remember that you just did an experiment that showed that the speed of a beam of light from your flash light (which is moving right along with you) was moving at the
speed of light... no matter which direction you pointed the beam.
As it turns out, no matter where you go, no matter how fast you are moving, a beam of light will always seem to be moving at the
speed of light relative to you.
But here is the kicker... someone else, moving at a different speed in a different direction would also measure the speed of your beam of light from your flash light as the
speed of light.
So what happens as you get close to moving at the
speed of light?
Do the experiment again, and you find that the beam from the flash light you have kept with you is still moving at the
speed of light relative to you. What has happened is that time has slowed down (for you) and distances in the direction of your travel have shrunk so that the
speed of light doesn't change for you.
Why is this needed/important?
The problem is that there is no universal reference frame. That is, there is no zero velocity spot in the universe by which the rest of the universe can determine how fast it is moving. As it turns out, rather than a zero velocity as a constant, we use the
speed of light as the universal reference. There is nothing (and no place) that is not moving relative to something else, but for all reference frames (everywhere) the
speed of light is the same.
So in our universe, how would you know if you reached the
speed of light?
As you get closer and closer, you shrink in that direction and time passes slower and slower (so that a beam of light will still seem like it is moving at the speed of light relative to you). Other things happen too (your mass increases), but you never reach the
speed of light because time (for you) ground to a halt.
You wouldn't notice any of that happening to you, but your friends watching you would see all that happen... and then go on with their lives.
If you don't get this, don't feel bad. We are used to nice, fixed coordinate grids when we think of space/geometry, and the fact that nothing like that nice environment exists in the actual universe make it a little disorienting for most everyone.