As best I can tell you is that the 'watch' mark puts an eyeball icon on a message and then any subsequent replies to that message come in also get the eyeball icon. This can be useful for threads of messages you want to 'keep an eye on'. Originally this was a newsgroups-only feature for keeping an eye on interesting threads but around TB 24 they added it for mail as well.
Putting a 'watch' eye is different from putting a 'star' on a message in that when you star a message, only that message is starred. Any subsequent replies/messages in that thread don't automatically get starred so you'd have to investigate your starred messages in some kind of threaded view to see if something new came in that was related. This is not always easy/convenient - not everyone uses threaded views daily for example (I don't) so this means another tab left open or remembering to explicitly check another view. Watched will show in any view (so long as the column for that icon hasn't been hidden/removed.)
Also, some people (myself included) want to use the star for other purposes. I use them for actionable items or those that I delegate to my assistant's attention which is only really possible because I don't need them for 'watch'. Yes, I could do it with tags (and back when, I did) but the star is more convenient and noticeable and frees up tags for our other (more appropriate imo) purposes.
There may be other advantages too that I'm not yet aware of but so far for me it's been a great feature addition.