When continental plates collide, the plate material gets folded and buckled up into mountain ranges.
A good example of mountains formed this way are the Himalayas. These mountains have formed as the Indian-Australian plate crashes into the Eurasian plate.
The continental plates share the same materials, just as two cars do. Imagine two cars colliding. What happens? The metal wrinkles and folds, forming mountains and valleys.
Tectonic plates react the same way to impact, except that it is a very slow-motion collision, taking millions of years.