I’m going to go out on a limb here and do no research whatsoever just so I can say that way back in ye Olden Days the City Watch (or police type people) would wander the streets at night ringing their bells and saying things like, “9 o’clock and alls well!” This told the people what the time was and that everything was well enough that some dude was still walking the streets and not being mugged.
So, having something you could carry around that would tell you the time was like having your own personal “watch” with you.
Yeah, that sounds pretty good. I expect this answer to be in Straight Dope any day now.