I'm an engineer, not a physicist, but I'll give it a go. You have a stack of boards, supported on the ends but not the middle. Lets say, for sake of illustration, the supports are cinderblocks. The striker will hit the top board and send the force downwards. The board that sees the most flexion is the board closest to the cinderblock supports. This is the bottom board which will bend until the structure breaks. Once the lower board breaks, the stress is relieved, putting the pressure on the next-lower board. The exceptions to this would be if the breaking materials have a spacer in between, or if the materials have a center score to make them easier to break.
This can be reproduced by anyone regardless of martial arts training:
Take four solid pieces of styrofoam, of equal size (cut up a cheapo styrofoam cooler if you like). Stack them on two hard supports like you were supporting boards for a break. Apply downward force to the top styrofoam "board". This can be done by pressing down on the top "board". It can also be done by putting a rock, a brick, a barbell, or some other small but hefty object on the top center. Watch how the individual boards bend, and eventually break.
There is definitely more than just the toughening of human tissue.
There are also the variables in the breaking materials. No two boards, for example, are exactly alike, and the ease in which they (or bricks, or blocks) can be broken depends on their moisture content, hence the concern many honest competitors have about unscrupulous competitors drying boards in advance. Ice can't be dried but it can be scored to break more easily. Ice has a crystaline structure that is cubical (3 dimensions) not planar (2 dimensions). When ice breaks, it shatters in many directions. It only breaks on a straight line if the structure has been physically interfered with, or has natural imperfections.
...
An article I found with a quick google search that explains the physics of breaking in a bit more detail.
http://tkdtutor.com/TOPICS/Breaking/Materials/Materials-03.htm
The article mentions speed. To be a bit persnickety, its more than just speed, its the vectors of velocity (speed, with a directional component) and acceleration (velocity over time). F=MA. Force equals Mass times Acceleration. I stress this not to pick a nit, but because the directional component is just as important as the speed. This is where training comes in, improving not just speed but the acceleration vector for a clean break.