The monoidal identity is the identity value for a particular monoid. A monoid must have an identity value and an associative binary operation. The identity value m is a value which makes no change to any other value n in that monoid, when n is combined with m using that binary operation.
1 is the monoidal identity for natural numbers under multiplication. 1 \cdot n = n \cdot 1 = n. 0 is the monoidal identity for natural numbers under addition. 0 + n = n + 0 = n