Watches are typically worn on the left wrist because the majority of people are right-handed and prefer to wear watches on the arm they use less frequently. There is no cultural significance associated how a watch is worn.
When most watches worked by wind-up clockwork mechanisms, wearing watches on the left hand made it easier for right-handed wearers to wind their watches. In contemporary times, wearing watches on the left hand is more of a personal preference. Watches are now worn on whichever wrist the user finds more comfortable, whether right-handed or left-handed. There is no particular benefit to wearing a watch either way.