You've probably noticed that there's more finger bling in this play than a Yo! MTV Raps video. Okay, maybe we're exaggerating. Technically, there are only two rings in this play (Bertram's and the King's), but they pass from finger to finger like nobody's business. Let's discuss.
Bertram belongs to a family of noblemen (French counts, to be exact) and the ring has been passed down to him along with the rest of his family's wealth and social status, which he inherited from his dead father. The ring is a family heirloom that's a symbol of Bertram's family lineage as well as his social status in France.
When Bertram is forced (against his will) to marry Helen, he refuses to have sex with her. He writes a letter explaining that he'll never be a good husband to her unless she can (a) get the ring off his finger and (b) get pregnant with his baby (3.2.2). Translation: When pigs fly!
Withholding sex is a lot like withholding the ring. Here's why: by denying Helen his family ring, Bertram is basically saying he doesn't think she's good enough to be married to him (probably because she's way below him in terms of social class). By refusing to have sex with her, he's also saying that he doesn't think she's good enough to be the mother of his child (a child that would eventually inherit all of Bertram's wealth, including the family ring). By the way, the king of France doesn't agree with Bertram. In fact, he gives Helen one of his rings as a gift of friendship after she cures his illness.
P.S. You may have noticed Diana's big speech about how her virginity is like Bertram's ring (4.2.8). Go read our "Character Analysis” of Diana if you want to know why...