A hand 扌 gripping — 巴 lends the sound. From physical grasping, 把 grew into Chinese grammar's most famous move: grab the object and put it BEFORE the verb.
The 把-construction is the rite of passage for every Chinese learner: 我把门关了 'I (took the door and) closed it'. It also counts things with handles — 一把刀 a knife, 一把伞 an umbrella, even 一把年纪 'a pile of years'.
A HAND grabs the object and drags it in front of the verb.
Linguists have written entire PhD theses on the 把-construction — no other Chinese word has generated more academic ink.