Spring power made portability possible. A weight-driven clock cannot be carried, but a coiled mainspring can power a timepiece in any position. Spring-driven clocks are recorded from the fifteenth century, and small portable versions followed.
The Nuremberg tradition. Peter Henlein of Nuremberg is often credited with the first watches in the early 1500s. The evidence for his role is limited, historians disagree about how far it goes, and objects attributed to him are contested. The fairer statement is that early portable timepieces were being made in southern Germany and northern Italy by the early sixteenth century.
Early watches were worn, not pocketed. These were drum- or ball-shaped cases hung from a chain around the neck or worn at the belt, with a single hour hand. They kept time poorly by later standards.
The seventeenth century made the watch a pocket object. Fashion changed around the mid-1600s, when waistcoats came into use, and watches moved into the pocket and became flatter. The balance spring was introduced in the 1670s; credit is contested between Huygens and Hooke. It improved accuracy enormously and made a minute hand worthwhile.
Later developments refined the form. They included jewelling (early eighteenth century), better escapements such as the lever, keyless winding in the nineteenth century, and factory mass production, above all in the United States from the 1850s. Together these made the pocket watch accurate, robust and affordable. It was the dominant personal timepiece until the wristwatch overtook it after the First World War.
In short: portable watches date from around 1500. Watches carried in the pocket belong to the later seventeenth century, and the familiar keyless, jewelled pocket watch belongs to the nineteenth.