It’s tradition to gift a watch to employees who have served you well and are retiring. So it’s easy to see Professor X commissioning this watch and presenting it to Wolverine one day. Of course that would make the Professor how old? Well, maybe in an alternate timeline anyway.
This is actually called the X-Watch and it’s a concept watch that should have been in the movie. It has numbers all along the length, and when they’re lit up it gives you the time. It also sports Braille so that the blind can use it. Or in case cyclops doesn’t have his visor handy and has to feel for the time.