This is Major Beau Biden. He served in Iraq and got a Bronze Star. He is Joe Biden’s deceased son. That is the Rolex that Joe Biden is wearing. He doesn’t owe anyone a reason anyway, but there it is.
EDIT: Later reports say that this isn’t Beau’s watch, but is actually a gift from Jill Biden and in honor of Beau’s memory. Either way, or even if Biden just went off and bought one for himself, any “stir” is manufactured outrage for no damn good reason. Joe Biden doesn’t need to justify having a fancy watch to anyone.
EDIT 2: I find that this answer has more responses than any I’ve done on Quora before. Darned if I know why. I’m seeing a surprising number of comments from people who are really into fancy watches – I guess I should have expected that – and from others who are either using this as an excuse to rant about Biden (I expected that) or say “this is not a big deal at all” (which is my point).