According to Sri Aurobindo and other integral theorists, the process by which the Divine manifests the cosmos is called involution. The process by which that which was created rises to higher states and states of consciousness is the evolution. The Involution is essentially up to the point of the Big Bang; the evolution is from that point forward.
Involution according to Sri Aurobindo
For Sri Aurobindo, Involution is the process by which the Omnipresent Absolute Reality loses itself in a process of self-absorption in multiplicity and inconscience The reason for Involution is Delight - the Delight of Being (the Spirit or Absolute) moving to Delight of Becoming (temporal existence, the cosmos), throwing itself into a multiplicity of forms, becoming lost in the inconscience of matter ((''Life Divine'' ch.11-12), and then through evolution the Delight of rediscovering the Spirit which had been hidden.
Involution according to Theosophy
In Theosophy and Anthroposophy, Involution and evolution are part of a complex sequence of cosmic cycles, called Round. When the universe attains a stage of sufficent density, the individual Spirit is able to descend and participate in the evolution. Involution thus refers to the incarnation of spirit in an already established matter, the necessary prerequiste of evolution.
Involution according to Ken Wilber
The integral philosopher Ken Wilber refers to Involution in his online chapter of Kosmic Karma, employing concepts from Plotinus, Advaita Vedanta, Tibetan Buddhism, and Sri Aurobindo. According to Wilber, the cosmic evolution described in his previous works is preceded by an Involution of Spirit into Matter. This Involution follows the reverse stages to the sequence of evolution - e.g. Spirit to soul to mind to Life to matter. Once the stage of as insentient, lifeless matter is attained, then "something like the Big Bang occurs", whereupon matter and manifest world come into concrete existence, from which stage evolution follows. take a brain sip!