When you see how a watch goes together, it is quite incredible that it can function as
@Sheff describes. Yes a quartz watch will be more accurate or a glance at a phone / smart watch will tell you all you need to know and do so much more but its the appreciation of how its made over anything I'd say.
This may help appreciate what's involved?
Depending on your stance, you can appreciate the workmanship, the history of the brand or as a status symbol.
EDIT
Also in a world where instant gratification seems to be more the norm, its nice to hark back to a simpler slower pace of life. Similar to where you see someone tinkering with an old car rather than having to rely on a garage to fix it for you by plugging in a computer.