Wrist instability occurs when one or more of the wrist ligaments have lost integrity, are lax, or damaged. The most commonly known ligaments are the scaphoid-lunate ligament and the luno-triquital ligament. The loss if ligament integrity alters the normal wrist mechanics of the carpal bones and hence affects your hand function. Injury occurs with a strong force (hyperextension or twisting), chronic loading of ligament, or repetitive forceful gripping.
In general, a complete rupture of the ligament could result in wrist arthritis if not treated properly. The ligaments are rich innervated with neural receptors, and hence affects your ability to know where your hand is in space-proprioception, as well as neuromuscular transmitters - telling your muscles when to move and how strongly or move.