Most of you have probably heard of the terrible Japanese earthquake and resulting tsunami. Tsunami warnings are still in place along the US West Coast as I write this post.
Tsunamis are initiated by processes that cause the displacement of a water column and can be produced by earthquakes, landslides, volcanic eruptions, etc. They do not behave like the waves you see on a beach. Tsunamis have very long wavelengths, typically 100 km or longer. They move very fast - often several hundred kilometers per hour. If you are on a boat in the open sea, you probably won't even notice as the ridge and crest of a tsunami passes.
A tsunami travels faster in deep water than in shallow water, and this is what leads to catastrophic inundation in coastal areas. As a tsunami approaches a coastal area, the wave slows, and water mass in the wave crest builds and deepens, leading to flooding at elevations above the normal sea level.
A remarkable animation of the 2004 Indian Ocean tsunami produced by NOAA is available here.