颊 is more literary than 脸蛋 (cheeks, colloquial). Common compounds: 脸颊 (cheek), 双颊 (both cheeks), 颊骨 (cheekbone). In everyday speech, 脸蛋 or 脸颊 are more natural.
页 on the right is the indexing radical, originally a stylised head-and-neck profile. It groups 颊 with other face and head words like 颜 (face), 额 (forehead), and 颈 (neck).
夹 supplies the reading, shifting tone from jiā to jiá. Its sense of two things pressing on either side fits beautifully: cheeks are the pair of fleshy panels pressed against the face, one on each side of the head.
