An identity will be true for all values that the variable can assume.
For example 2(x+3)=2x+6 is true for all real numbers. If the equation is an identity you will be able to perform operations such that the end result is 0=0. In the example given we use the distributive property on the left hand side to get 2x+6=2x+6; subtracting 2x and then subtracting 6 from both sides yields 0=0.
An example of a trigonometric identity is `sin^2theta + cos^2 theta =1` which is true for all values of `theta` .