Not to be confused with a chronograph, a chronometer is a watch that has been tested and certified to be incredibly accurate by some sort of governing body. The most prominent example of that today is the Official Swiss Chronometer Testing Institute (COSC), which is responsible for testing Swiss-made chronometers; only the COSC can deem a Swiss watch worthy of “chronometer” status, though other countries have their own chronometer testing outlets, like the Glashütte Observatory in Germany. While quartz watches can also be certified as chronometers, the term most often refers to certified mechanical watches that are accurate to within just a few seconds per day (as an example, COSC-certified chronometers must accurate to within -4/+6 seconds a day). Some brands, like Rolex and Omega, do their own, more stringent, certification programs in addition to COSC testing… More at Gear Patrol.
It is a common question that never goes away and one that is understandably difficult for all of us to understand. Collectors will spends many thousands of pounds extra to get a mechanical watch that is more accurate than others, but which is no way near as accurate as an Apple Watch or most quartz watches. Even I struggle with this.