In his various discussions of Centering Prayer, Thomas Keating often uses the term "False Self." This term has also been used by other writers including Thomas Merton, Richard Rohr, etc. Each author uses the term in a slightly different way.
For Keating, the False Self is created when we experience emotional trauma throughout our lives. As we experience wounding in areas of our core psychological needs (for Keating, these needs are summarized in the categories of power/control, esteem/affection, and security/survival), we develop attachments to people, places, and situations that bring us comfort, and aversions to people, places, and situations that lead to discomfort in the light of these wounds.
This collection of attachments and aversions results in what Keating calls "emotional programs for happiness."
A young child overhears his father saying, "I wish he was more like his brother," which attacks his core psychological need for esteem/affection. The incident then becomes buried in the boy's subconscious. He may not even remember the incident in adulthood, but, on a subconscious level, part of him continues to want to imitate his brother to achieve his father's affection. The "emotional program for happiness" of "needing to be like my brother" becomes a deep part of who he is. As a result, he develops attachments to things that make him more like his brother, and aversions to things that make him different. These attachments and aversions, at least in part, continue to drive his behavior throughout life.
On this model, each human being has a host of emotional programs for happiness running at the same time, each based on our unique traumas. These programs create anxieties as we interact with the world, and may even conflict with each other.
For Keating, the False Self is our wounded self; and our self that searches for things in the world to help us deal with those wounds.
The solution, for Keating, is experiencing the "Divine Therapy" through Centering Prayer. As we get deeper into our practice and become more open to the presence of God, these incidents are released from the subconscious and we eventually become healed of our traumas. Keating calls this the Archaeological Dig. The result might be what Keating would call our True Self, our healed sense of self that has our core needs fulfilled through the presence of God.
For more on Keating and Centering Prayer, check out the Centering Prayer page of the site.