The absolute definition is that the molecule must not have a center of inversion or an improper rotational axis. All shapes can be described by a 'point group' which describes all the information about the molecules symmetry.
This is a branch of a mathematical field called 'group theory', and is well beyond my understanding being only a chemist. It is used in chemistry to simplify many problems to trivial calculations, such as calculating the number and nature of vibrations within a molecule.
It isn't very hard to get to grips with some of the symmetry operations (eg a plane of symmetry or a rotational axis) and there are many good websites with animations to help visualize them. Try searching molecular symmetry