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).
木 (wood) is the indexing radical. A 柄 is a handle — most traditionally a wooden shaft on an axe, hammer, knife or umbrella. The wood radical groups 柄 with 杆 (pole), 棍 (stick), 把 (grip — also 扌-radical) and other tool-shaft words.
丙 (bǐng) supplies the sound, unchanged. 丙 is the third of the ten 天干 heavenly stems and rarely carries meaning of its own in modern compounds. Same phonetic series: 病 (illness), 饼 (cake), 炳 (bright).
