An example of elastic force is bungee jumping. The elastic cord creates resistance and imposes a force when the cord is stretched far enough. That elasticity creates the bouncing motion a bungee jumper feels after the initial jump, while the cord works to return to its normal size.
Elastic materials, such as a bungee cord, resist the pulling and changing of its shape. The farther the elastic is stretched, the more force it exerts to return back to its original shape. The jumper is being pulled down to the ground by gravity, and the cord, resisting and trying to pull back to its original shape and length, is exerting the elastic force.