What does it mean when a man gives a woman a watch?

could mean anything from "I really value you" to "you're always late".

You could always talk to him about it but if you don't want to perhaps you could do some research on the watch, perhaps find out how expensive it is or the story behind it, this may help you deduct the thoughts he was having when he considered buying it for you.

Of course I would put talking to him about it as a first option.