What is jewels in a wristwatch?

Industrial-grade or synthetic rubies are used to make a watch movement's bearings. A pair of these ruby 'jewels' hold the ends of the staff (axle) for each major wheel (gear); You can see some of these on the surface of the movement as tiny red doughnut shapes. The balance wheel, the most active moving part in the watch, usually has two jewels at each end of its staff; each pair fit together to form a single bearing with an oil-filled reservoir inside.

Rubies are almost as hard as diamonds. As long as the watch is properly lubricated, these smooth bearings are nearly friction-free, and are largely responsible for the many years of faithful service a mechanical watch can provide.
The ticking of a watch is the sound of two small jewels, each about the size of a pinhead, smacking into the steel teeth of the escape wheel. The loudness of these tiny rubies striking against steel hints at the huge stresses acting on these parts, relative to their size.

It's important to have a watch serviced about every five years. The ruby bearings are much harder than the steel parts they mate with; without oil, the steel will rapidly be ground away.
The jewels are not precious and have no value as jewelry; they're generally worth only a few cents each. There's no need to fear that a watch repairer will steal them.