Collisions are when two objects bang into each other. An example is when you play pool. If you're really good, you'll be able to actually aim the stick well enough so that the white ball hits another ball on the table. When that happens, you get a collision. There are two extreme versions of collisions. Totally inelastic collions, and elastic collisions.
Totally inelastic collisions are when the two objects the hit each other stay in contact. Think about two pieces of chewing gum being thrown at each other and sticking. On the other hand don't. It's too disgusting.
When a dropped superball hits the ground, it bounces up to almost it's original height. That's the opposite case of an elastic collision. In both cases the actual collision process is quite short. Often of the order of milliseconds. We'll try to understand the process of the collision now in a little more detail.