Pivots are the fine ends of arbors that turn in the plates. Fitting a jewel as the bearing reduces friction and wear, because the steel pivot runs against a hard, polished stone rather than brass.
Seventeen jewels became a common standard for a fully jewelled time-only watch: the balance, escapement and train pivots are jewelled at the points of greatest wear. Earlier and cheaper watches often had seven or fifteen.
Since the early twentieth century, most jewels have been synthetic corundum (ruby or sapphire). They are functional parts, not gemstones of meaningful value.
A higher count does not automatically mean better quality. Some automatic watches of the mid twentieth century added jewels that did little in order to advertise high counts. Later industry rules limited what could be counted.