Power
Time, along with space, gravity, and your Aunt Florence's chili recipe, is one of the most powerful forces in the universe (that is, if you believe it exists). If you think you have any hope of controlling it, you're doing this career wrong. The horologist doesn't control time any more than a sea captain controls the ocean. What you do instead is measure it, define it, and let everyone else know what those measurements and definitions are.
The pieces you'll build or work on help humans understand the difference between now and then. Sure, you might know it's generally time to eat because your stomach is growling, but the only reason you're not late for your lunch meeting is because of the little hand and the big hand.
The power you exert is over the mechanics of measuring time. This is important to anyone who ever has places to be and wants to get there when they're supposed to. The simple act of knowing the time means that people have to rely on tools to keep them on track. Otherwise they'll miss important things like meetings, appointments, and second period math class (you know who you are).
We realize that smartphones, tablets, and other 21st-century technologies have rendered the wristwatch nearly obsolete, but that doesn't mean clocks and other time devices are going anywhere any time soon. Just look around and you'll still see them everywhere, from vehicles to public buildings to that one on the classroom wall that you think keeps slowing down.