As a theory of personality, Transactional Analysis (TA) provides one approach to how people are structured psychologically. To do so it uses a three-part model known as the ego-state model. The same model is used to give one understanding to how people function - how they express their personality in terms of behaviour.
TA can also be perceived as a theory of communication. This can be extended to give a method of analysing systems and organisations.
TA is also one of the theories of child development. The concept of life-script gives TA's explanation how our present life patterns originated in childhood. Within the framework of life-script, TA develops explanations of how we may continue to replay childhood strategies in grown-up life, even when these produce results that are self-defeating or painful. Thus TA can also be perceived as a theory of psychopathology.
Read more about Transactional Analysis here.
Wikipedia provides more thoughts about transactional analysis. This link does not imply CTPDC's endorsement of what is found on that webpage.