Here's a perfectly reasonable and rational explanation. Your character is married. Married people wear rings. Therefore your character wears a ring. The ring, in order to appear on your character, needs to be an equitable item. After you come out of the vault they don't take it away. A disappearing ring would make no sense so you get to keep it.

Anything beyond that is wild speculation.

Whike we are on the subject of rings, do you think there are other rings or is this the only instance?

http://www.gamesas.com/topic/1523120-jewelry/

Hell their better be, I find it amazing that F3/NV had very little rings to equip.

TES didn't invent rings, Beth! Give us more rings :I

The ring could possibly effect the story later on. Maybe for example you find your son/spouse, and must show who you are because they don't trust you to be the real one with all the androids running around. That would be crazy..

Man, the Lone Wanderer's parents were brutal.

i can't wait to see how well it flies after being exploded

That was actually pretty funny.

Hypothetically, it could be a clever way of designating your availability for romance, as has been said. Certainly a lot more organic a process than they invented for Skyrim. Want to romance a character or mark yourself as available? Just take off your wedding ring.

I do wonder if it's going to have any further gameplay repercussions at all. We'll just have to wait and see...

It could be for RP functions. Maybe when the Vault-Tech Salesman comes to your door he asks if you're married or single and if you pick "Married" the wedding ring will be equipped if you pick single, you have no ring and your spouse is just a girlfriend/baby mama/gay coverup which really plays into RP a bit better.
Also, it could be possible to force romance while wearing the ring for negative Karma.