柄 appears in many compound words: 刀柄 (knife handle), 伞柄 (umbrella handle), 把柄 (leverage/something to hold against someone). The figurative meaning "power/leverage" comes from the idea of gripping a handle.
grammar
柄 also functions as a measure word for things with handles, like swords or umbrellas: 一柄剑 (yì bǐng jiàn, a sword).
