What’s the difference between quartz and mechanical/automatic movements?
The movement - the inner workings of the watch - is what makes up the main timekeeping mechanism. Most watches have either a quartz movement or a mechanical movement. The type of movement you choose depends mostly on one's taste.
Mechanical movements are a tribute to the watchmaker's art and monitor the passage of time by a series of gear mechanisms. When a mechanical movement does not have to be wound, it is known as an automatic movement. These self-winding movements are wound by the movement of your wrist. (No, you don't have to shake it to work! The normal, everyday movement of the watch on your wrist charges the winding reserve.) When this type of watch is removed from your wrist the movement winds down in 10 to 72 hours, depending on the size of its winding reserve.
Quartz movements, on the other hand, are powered by a battery and do not stop working once removed from your wrist. When activated by a battery or solar power, the thin sliver of crystal very predictably vibrates at an extremely high frequency (32,768 times per second), thus providing very accurate timekeeping. The battery in a quartz watch generally needs to be replaced every 1.5 years, unless stated otherwise by the manufacturer.