The physics behind a hockey check is fairly simple. It is a basic collision. One force, the checker, is coming in with a mass and acceleration, onto and another player with a separate mass and acceleration. As Newton's law states, every action has an equal and opposite reaction. So the player with a bigger mass will be able to absorb more of the hit, and a smaller player, much less so.
The Player who was hit will stay in motion unless acted upon by an outside force. A lot of times this is the boards. Many injuries occur by players going into the boards with a lot of force. The boards are unforgiving and do not have a lot of give meaning a short impact time witch means a lot more pain for the person being checked.
However if a player is against the boards, he will be much safer when checked. The collision force would be transferred from the player to the boards back to the player and back to the original checker. For example, if a player gets hit by a 20N force, he will then transfer 20N to the boards but some of that force would come right back because of a recoil. This is why you often see the original checker fall down after making a check on someone who is along the boards.
Lastly the players momentum is the ultimate determinate of the strength of the check. Momentum (p=mv) is constantly changing while on the ice. The players mass is a constant, so in order to increase their momentum, players will go faster. Higher velocity means more momentum, means bigger collision.
Checking is an important part of the game and is all just applying forces to other players. So in conclusion, in order to deal the biggest hit, you want to maximize your mass and velocity, and when taking a hit, try to have the boards absorb the hit rather than just you.