Bonding is a two-way, lifelong link. The dragon picks the rider — not the other way around — and once the bond forms, the rider develops a signet, a personal magical power that shows up differently for every rider.
Cadets don't get to choose a dragon. The dragon chooses them, and plenty of cadets die before a dragon ever looks their way. Being picked is rare, and it is dangerous to even reach the point where a bond can happen.
The bond unlocks a signet. Violet's signet is rare — she can wield lightning. Xaden's lets him control shadows. Every rider's signet is unique, a reflection of who they are.
Dragon and rider talk in each other's heads. In Violet's case, the bond between Tairn and Sgaeyl means she can reach Sgaeyl too, which is part of why her connection with Xaden runs so deep.
Dragons are not animals to be owned. They are equals, often the more dominant partner. A dragon's death is catastrophic for a rider, and riders protect their dragons with their lives — the feeling is mutual.