The vertical-heart radical on the left marks 愉 as an emotion, pleasure or gladness felt inside. It indexes the character with the emotional family: 怕 fear, 情 feeling, 怀 cherish, 快 happy. Every inner-state verb of feeling carries this radical.
俞 supplies the sound yú unchanged. It also adds a soft semantic flavour: 俞 originally meant assent and agreement, the "yes" said by an elder, and pleasure is the heart's assent to a situation. Same phonetic in 偷 steal, 输 lose, 愈 heal, 逾 exceed.
