Person centred therapy was developed by Carl Rogers who worked in the field of psychology and was interested in finding ways to support people and help them get through their difficulties. He believed that one important factor in this was the relationship between the patient and the therapist (the therapeutic relationship). He believed the relationship needed to be balanced in power and in a time when those seeking support were referred to as "patients" his clients were given the respect of being called just that and he instead showed them that the answers lay within the clients themselves - not with what the therapist believed. This approach helps clients help themselves and find a strength within that for many reasons they were unaware of.
Carl Rogers believed that humans have one basic motive, that is the tendency to self-actualize - i.e., to fulfill one's potential and achieve the highest level of 'human-beingness' we can. Like a flower that will grow to its full potential if the conditions are right, but which is constrained by its environment, so people will flourish and reach their potential if their environment is good enough. A person enters person centred therapy in a state of incongruence. It is the role of the therapists to reverse this situation. Rogers (1959) called his therapeutic approach client-centered or person-centered therapy because of the focus on the person’s subjective view of the world.
The Therapist and the client are equal partners in Person Centred Therapy. Unlike other therapies the client is responsible for improving his or her life, not the therapist. This is a deliberate change from both psychoanalysis and behavioural therapies where the patient is diagnosed and treated by a doctor.
Instead, the client consciously and rationally decides for themselves what is wrong and what should be done about it. The therapist listens and encourages on an equal level, challenging when necessary but always providing unconditional positive regard.
Here is a short video with Carl Rogers explaining how acceptence, understanding and empathising with the client can lead to change.