Product Cipher is a cipher that composed of both #substitution (S-box) and #permutation (P-box). Introduced by Claude Shannon, it is the backbone for the modern Block Cipher. It provides diffusion and confusion of message and key.
The diffusion is done by the P-box (with the help of special function) which disperses statistical structure of plaintext over bulk of ciphertext, meaning each single plaintext could affect many ciphertext bits. S-box is responsible for making the relationship between ciphertext and the key as complex as possible, preferably non-linear relationship, thus forges confusion into the message and key.