A quartz movement is essentially another way of saying a timepiece is battery-powered. In simpler terms, a quartz caliber operates via an electrical current from a battery that gives power to the quartz crystal within the movement. This causes it to vibrate, and these vibrations cause the movement to oscillate, which drives the motor. Finally, we see this in the moving hands on the face of a watch. One main advantage of a quartz caliber is accuracy. Quartz movements are far more accurate than mechanical movements. Another benefit is convenience. Aside from a battery change every couple of years, a quartz watch will continue to run without the need to wear it or wind it.
Automatic movements are complex devices made up of a mainspring and trains of gear. They are often composed of hundreds of tiny and intricate parts. When you are wearing an automatic watch, the movements of your arm cause an internal moving weight to rotate and transfer energy to the power reserve. You can also gently shake the watch from side to side to cause the weight to rotate and ‘power up’ the reserve. If you wear the watch continuously (even if you take it off for a day or so, depending on the power reserve), it will continue to run just from the power it stores up while you wear it.