As a tsunami wave approaches the coast (where the sea becomes shallow), the trough (bottom) of a wave hits the beach floor, causing the wave to slow down, to increase in height (the amplitude is magnified many times) and to decrease in wavelength (the distance from crest to crest).
At landfall, a tsunami wave can be hundreds of meters tall. Steeper shorelines produce higher tsunami waves.
In addition to large tsunami waves that crash onto shore, the waves push a large amount of water onto the shore above the regular sea level (this is called runup). The runup can cause tremendous damage inland and is much more common than huge, thundering tsunami waves.