When two bodies collide some of the energy that they carry can be used to deform them or might be dispersed in the form of heat, or maybe the loss of energy is small enough to be neglected.

If the total kinetic energy is conserved in the collision of two particles, then the collision is considered elastic. In this case, conservation of linear momentum and kinetic energy completely determine the velocity of each particle after the collision. 

Although we cannot say that there are totally elastic collisions in nature, there are many cases in which the variation of energy in a collision is so small that it cannot be detected. In these circumstances, we will consider the collision elastic.

In the following visual we will observe a frontal collision of two billiard balls that satisfy the conditions of an elastic collision.