Planck's (love the name btw) explanation is perfection, so there's nothing more I can really add - except two analogies that might help.
Special relativity: imagine that you are in a car, and I am standing beside the road watching you approach. You are travelling at 50mph, and as you pass me you throw me a ball that's travelling at 20mph. We can calculate fairly simply that the true velocity of that ball is 70mph - in the car it was already travelling 50, you added another 20 with the force that you used to throw it.
Yes? But what's extremely weird is that the light coming from the headlights on your car behaves in an entirely different way. No matter what speed you are or aren't travelling, light will zoom away from you at exactly the same rate. If you are in motion, you do not add on the 50mph that you are already travelling, and when you stop, you do not subtract it.
So, this tells us that light (in a vacuum, provided it is unimpeded) travels at exactly the same rate no matter who is watching or how fast they are travelling.
Now, to work out the speed of anything you would divide distance by time taken - and Einstein realised that if speed does not change, something else must. And he postulated that it is time that changes (relative to an observer).
This essentially means that the faster you (or anything) travels the more time will appear to slow down to anyone watching your progress. If you are on a train, and I am sitting on the platform, and I watch you coming past at, say, 80% the speed of light - I would notice if I looked in the window that you were moving quite sluggishly and any clocks on the wall would be moving slower than my watch. It would be a bit like watching a video slowed down. But, you wouldn't notice anything different at all - it would all be entirely normal from your perspective. But if you happened to look out at me, it would be me that was moving slowly and sluggishly etc. There is, therefore, no way whatsoever to know which one of us is actually speeding and which one is stationary - it's all relative.
General relativity: this is all about the inextricable way in which space and time are bound up together, and how gravity is a product of this.
Envisage spacetime as a rubber sheet stretched between two people. In the middle rests a cannonball, which causes the sheet to sag a bit. If a third person takes a smaller ball and rolls it across the sheet it will try to move in a straight line as Newton's law of motion predicts, but will be drawn into the dip made by the bigger ball.
That, essentially is how gravity works - large bodies of mass (like the sun) cause a dip in spacetime which attracts smaller bodies (like the earth).
:-)