Saw this posted on Reddit and found it was easier to intuitively understand than most demonstrations or explanations. Think of the shore as being on the right side of the image. The wave is the top illustration, and the tsunami is the lower illustration.
And, just because it's incredible and people don't understand unless they see it, here are links to some videos:
The thing to remember: IT JUST KEEPS COMING. More water, then more. It's not the force of it that kills, it's the sheer volume. People successfully outran the waves, but if they stayed too long they were dead.
A pilot has a report of what happened in the air during and after the earthquake.