A signet is the magical power a rider develops after bonding a dragon. It does not appear instantly and it is not chosen — it emerges from the rider, and no two riders end up with exactly the same one.
Violet's signet lets her wield lightning. It is rare and powerful, and it marks her as someone to watch in the Riders Quadrant despite her physical weakness.
Xaden's signet lets him control shadows. It suits his reputation as someone who operates in the dark, and it makes him one of the most dangerous riders in the Quadrant.
The signet is the payoff of the bond. It is why dragons are so central to the story — without a dragon, there is no power, no rank, and no future for a rider.