A quartz watch is one that runs on battery power and is regulated by a vibrating quartz crystal. They are comprised of computer chips, electronic components and few or no moving parts. Quartz watches are extremely accurate and can have an assortment of exciting functions including alarms, stopwatches and more.
Mechanical watches fall in to one of two categories—manual-wind or self winding, also known as automatic. While these timepieces are less accurate than their quartz counterparts, they are prized and enjoyed for the ingenuity and precise technical skills of the highly trained watchmakers that hand assemble them. These contain jeweled movements with many parts, sometimes in the hundreds! In automatic watches, the power is generated by the motion of the wearer, thus not requiring winding or changing of batteries. The labor-intensive aspect of mechanical watches make them substantially more expensive and collectible than their quartz counterparts.
Digital vs. Analog
Digital watches have LCD displays and are virtually always quartz. Analog watches have the more traditional display with hour, minute, and sometimes second hands; they can be either quartz or mechanical, or other "hybrid" technologies.
Chronograph vs. Chronometer
A chronograph is any watch with stopwatch or timekeeping capabilities. In analog models, these often have sporty looking sub-dials, which track the passing of time.