An identity is an equation that holds true when any value is plugged into the variable where the expressions on each side of the equation are defined.

Example Identity 1:  sin^2(x) + cos^2(x) == 1

Plug in any value for x above and the left hand side = right hand side.

Example Identity 2:  tan^2(x) + 1 == sec^2(x)

Plug in any value for x above where tan(x) and sec(x) are both defined and the left hand side = right hand side.