An example of a perfectly elastic collision is that it doesn't exist. But for the sake of saying it exist you would assume that a collision takes place where energy is completely conserved and is not lost as (non-usable energy) heat. Maybe you say that a gas molecule collides with a completely (perfectly) smooth surface and the gas molecules collides perpendicular to the surface (does not collide at an angle). The gas molecule then bounces off the wall with the same speed as when it colliding against the wall. This would assume a perfectly elastic collision as KE=1/2mv^2. When your gas molecule collides its mass doesn't change but when you say that the gas molecule had the same velocity when it bounces off the wall you ahve assumed that kinetic energy is maintained (which assumes perfectly elastic).
