Normally one would this question only if one believed that there is a Conscious Being or Power that has gone into the making of this world. If one is an Atheist then the right question would be not why but how this world was made. Because non-belief in a Conscious Wisdom and Force that has gone into creation implies that there is no real purpose in creation. In that case one has to adopt one of the three standard theories, each incomplete and unsatisfactory as the other.
1) The Vedantic theory that there is no real purpose but simply a play of Nature or Maya that creates the illusion of a world due to false perception. The only purpose then, of the individual, is to get out of the illusion, Moksha.
2) The Buddhist theory that is very similar to the Vedantic except that it replaces the Vedantic Idea of a Purusha that is beyond the creation with very little to do with it, with the Buddhist Idea of a Nihil or Nothingness Beyond this world. This world is a world of suffering and the only purpose is to find an exit door and come out of it, Nirvana.
3) The materialistic theory that there is either no Creator or else IT is an Unknowable X. The only purpose therefore is to study the laws of Nature and make life better.
According to Sri Aurobindo the world is a distorted expression of the Divine who is at the origin and the core of creation and everything. The purpose therefore is one with the aspiration common to every human being, which is to find and express higher and higher Perfection through constant progress.
Affectionately,
Alok Da
