Even though I have never done karate myself, in the past I have seen many karate videos of people breaking concrete bricks and wooden boards with their bare hands. Looking at a basic principle of physics helps to understand how people can pull off these impressive moves.
Since F=ma and Momentum = mass x velocity, force and mass are positively related. When trying to break a board, force needs to be transferred as fast as possible and the person also has to use as much of his or her body mass in the motion as possible.
In addition, the extension of a person’s arm is crucial to breaking the board. Since momentum and velocity are also positively related, the extension point at which the person’s hand hits the board must maximize velocity. Therefore, his or her arm must not be fully extended. Rather, it should be at a point of extension in which the hand has a positive or zero acceleration.
Finally, the person must attempt to exert as much force per square inch on the board as possible in order to break it. That is why hitting the board with the side of the hand is much more effective than hitting it with the palm.
By using the side of the hand, learning to efficiently channel body mass, and finding the optimal point of arm extension, one can plausibly break a board with lots of practice.