When Twinsen meets Johnny Rocket, he tells him to go to a dissident meeting, and gives him the ring. Twinsen must show the ring to the attendant in the Twinsonian Souvenir Shop to get to the meeting. Later, when Queen Astrid asks for a sign of good faith, Twinsen must show her the ring.
"This ring is made and worn only by the dissidents. It is their secret identification sign and it will allow you to be recognized as on of them and to make contact with them."