What is meant by elastic and inelastic collision?

The collision in which total linear momentum and total K.E. is conserved is called elastic collision.

i.e. In elastic collision,

                m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

                ½(m₁u₁²+ m₂u₂²) = ½(m₁v₁² + m₂v₂²)

Eg: Collision between atomic or sub-atomic particles, collision between gas molecules, etc.
The collision in the total linear momentum is conserved but the total K.E. is not conserved is called inelastic collision.
i.e. In inelastic collision,

                m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
But,
                ½(m₁u₁² + m₂u₂²)  ≠ ½(m₁v₁² + m₂v₂²)

Eg: A bullet embedded in a target is one example of inelastic collision.