Tsunamis happen for numerous reasons but a subduction earthquake is very good way to generate one. What happens is the sea floor either rises or falls and all the water above it rises or falls too. This displaces a lot of water and creates a wave that extends all the way to the sea floor, so if the ocean depth at the epicenter was say 2 miles then the wave amplitude was 2 miles and the force of the wave would be proprosoinal to the amount of water displaced. As the wave travel towards the shore the depth of the water lessen and the wave shape changes to match, as the wave hight lessons the wave lenght increases, in other words in stead of being 2 miles tall and 10 feet wide it becomes 10 tall and two miles wide. Of course it is losing energy the entire time so farther away it might be 2 feet tall and one mile wide.
Anyway we have all seen a big swell roll in, but that big swell was maybe what 50 or 100 feet wide? This wave (wave series) was a kilometer or more wide. So when it hit land it just kept going, being pushed by the mile of water behind it. Like a huge flash flood, a mile long wall of water ten feet tall traveling at 30 mph, hitting and entire coast line all at once. Not a good day. And that's what happened at Thailand, imagine poor Indonesia where the wall of water was 25 or 30 feet tall.
Seeing that poor mother run to her doomed family is heart breaking. Maybe a miracle happened and they all lived, poor fools, when all the water drains away from a coast line run like hell to higher ground, do not go play in the mud!