Left indexing hand radical 扌 - left-side variant of 手. Anchors 挥 in the hand-action family alongside 打 (hit), 拉 (pull), 推 (push), 抓 (grasp). Waving, brandishing, and commanding are all motions performed with the hand.
Right 军 supplies the sound (jūn -> huī through j/h alternation in Old Chinese, attested in 军/挥/晖/辉 phonetic family). 军 itself depicts a chariot 车 under a covering - an encampment. Lends a faint command-flavor: an officer waves troops into formation. Same phonetic: 辉 (radiance), 晖 (sunshine), 浑 (murky).
