Puissance is the power to influence what other people do or believe. A celebrity who is extremely popular with teens has puissance to help end problems like bullying just by talking about it in interviews.
Puissance is a French word that describes being powerful. When you have a strong influence over someone, you have puissance. It's an uncommon but poetic way to describe power, especially the power to convince someone to do something, like an older sibling's puissance. Another meaning of puissance is a show jumping horse's ability to jump large hurdles.