Storing energy in a spring is a common feature of mechanical devices. There is a spring that keeps the door knob in the right position, so that the door will not come unlatched by accident; when we turn the knob, we transfer a small amount of energy to it -- more than a breeze or an insect or even the cat is likely to possess.
As we close the door, the latch tongue is pushed in by the strike plate against a spring, storing enough energy to push the tongue back into the jamb when the door is fully closed.
For still other examples, the keys on a computer keyboard, a stapler, the clip of a safety pin, and the mechanism of a retractible ball-point pen all rely on a spring and its ability to store energy, to push them back to the starting position.
The mechanism being used in this activity to launch the ball is different in form but identical in concept to a bow and arrow: elastic energy is stored in a spring, which is then transferred to a projectile, where it appears in the form of kinetic energy.
The ride stuff
Riding a bicycle on a level road is easy. You put a little energy in to get up to speed, and then just coast. There's a tiny loss of energy to the air and to the tires that you need to replace, but it's easy riding.
Riding a bicycle up a hill is hard work! As the bicycle moves forwards, it is also getting higher, and thus we are increasing the gravitational potential energy. When the hill is not very steep, the amount of energy needed to advance 1 meter is small; on a steep hill, it is larger.
But once you get over the top of the hill and are on the way back down, all the energy you invested is being returned to you. Riding downhill is easy and fun. From the point of view of the energy involved, the hill doesn't matter at all: you put some energy in and then get it all back on the way down.