Left person radical, the side form of 人. It anchors 傅 in the people family — a 傅 is a tutor or mentor, a person who guides another. Same radical pattern shows up in 你, 他, 们, 体, 信 and most words that name a kind of person or interpersonal action.
Right side is 尃, an archaic graph meaning 'to spread out by hand,' supplying the sound fū → fù. The same phonetic appears in 博 broad, 搏 grapple, 缚 bind, 薄 thin. Faintly semantic too: a tutor 'spreads' knowledge outward to a pupil, fitting the master-craftsman sense of 师傅.