As an example, the field of real numbers is not algebraically closed, because the polynomial x2 + 1 has no real zero. By contrast, the field of complex numbers is algebraically closed, which is the content of the fundamental theorem of algebra.
Every field F has an "algebraic closure", which is the smallest algebraically closed field of which F is a subfield. Each field's algebraic closure is unique up to isomorphism. In particular, the field of complex numbers is the algebraic closure of the field of real numbers.