What does transcendental mean in mathematics?

An algebraic number is one which is a root of a polynomial equation with rational coefficients. All rational numbers are algebraic numbers. Irrational Numbers such as square roots, cube roots, surds etc are algebraic but there are others that are not. A transcendental number is such a number: an irrational number that is not an algebraic number. pi and e (the base of the exponential function) are both transcendental.