In simple terms
By listening to that inner calling and pursuing your dreams, you can individuate and live a happy, fulfilled and self-directed life of authenticity and purpose.
In short: it is the process of becoming self-actualized.
[Huffington Post – The Individuation Process: Finding Your True Authentic Self]
In more detail
from from Scott Jeffrey:
Jung believed each person is unique and has a distinct destiny.
Most of Jungian psychology—also called analytical psychology or depth psychology—centers on what Jung later called the individuation process.
The individuation process was Jung’s way of explaining the path to optimalpersonal development for an individual.
Jungian analyst Anthony Stevens writes in Private Myths:
Individuation is the process, simple or complex as the case may be, by which every living organism becomes what it was destined to become from the beginning.
In Jungian psychology, individuation is the process where the individual self develops out of an undifferentiated unconscious – seen as a developmental psychic process during which innate elements of personality, the components of the immature psyche, and the experiences of the person’s life become, if the process is more or less successful, integrated over time into a well-functioning whole. [Wikipedia]