Well, since I don't know your level, let me go down as low as possible for me and try to explain. The deficiency is mine, not yours, if you don't understand!
You know momentum is the product of mass and velocity. Since mass of a given object is constant, the higher the velocity the greater the momentum and when it is suddenly stopped, the greater the impact!
You also know that kinetic energy is 1/2 m.v^2. So, the higher the velocity of an object of mass m, the higher the energy and higher the momentum. Also remember that both energy and momentum are conserved. Energy gets converted into some other form. Momentum gets transferred from one body to another.
Try this simple experiment. Get a rubber ball, not very hard nor very soft, medium. Throw the ball against the ground or against a wall. Throw with different speeds and observe the impact on your palms when you try to catch it on rebound. With higher momentum, the impact on your palms will be higher. You will be observing something similar when you are running and suddenly run into a wall or another person. The faster you are running, the more will be the shock and impact.
If you are playing baseball, you will be able to relate immediately when you try to catch a powerful shot or just a simple throw. The palms need to absorb much more impact in the first case when the batter hits it. You wear gloves to absortb that excess momentum, you move your hands back to reduce the shock.
Finally visualise a small ball hitting the earth and a plane crashing into the ground or a 1000 kg bomb falling from a height. Why the destruction is so much more in the later cases? Due to the higher momentum which has to be absorbed by the earth and any people there.
Hope you got a better idea now than a few minutes earlier.