What is the meaning of Identity_element?

An element of an algebraic structure which when applied, in either order, to any other element via a binary operation yields the other element.

a left identity if ${\displaystyle i*x=x}$ for any ${\displaystyle x}$ in the structure,

a right identity, ${\displaystyle x*i=x}$ for any ${\displaystyle x}$ in the structure,

simply an identity element or (for emphasis) a two-sided identity if both are true.

Source: wiktionary.org