It allows the users to connect themselves via an invisible link to their target, preventing him/her from escaping until the Anchor's owner releases them. The anchor initially appears as a red whip (purple in Vetrix's case), before fading once it has anchored to the target's wrist. The owner can disconnect the link, but the target cannot.
The Duel Anchor can also be used for other purposes. Kite used it as a rope, which was grabbed by Yuma when Kite and Dr. Faker nearly fell to their deaths.