What's the difference between elastic and inelastic collisions ?

Well it all depends on how the energy of the moving objects is transfered during the collision. In a elastic collision, first the objects are moving toward each other with both a certain kinetic energy, then they collide, and when they rebound, all the kinetic energy is still there, except it might be reparted differently between the two. Pool balls typically collide in elastic collisions. 

For inelastic collisions, the kinetic energy is not only going to be transfered, it's also going to be transformed. For example if one of the object is deformed during the collision, it requires some energy. That energy is no longer kinetic energy, so the total kinetic energy of the system has gone down. It means that we can't use conservation of kinetic energy to solve the problem