The letters stand for the education the therapist undertook (MA Hons, Bpsych Hons, PhD, etc.) and the professional bodies the therapist is registered with (HCPC reg, UKCP reg, MBACP Accred, etc.).
The letters also give hints as to how long the therapist has been in practice. For example, with the British Association for Counselling and Psychotherapy (BACP), a therapist with reasonably long-term experience will have the “MBACP Accred” after his or her name. But if they have “MBACP Sn Accred” after their name, the “Sn” refers to senior, and means they have extensive experience and a specialist area they are accomplished in.
Want to know more? You can find out what each set of letters means by going to the websites of each professional body, or read more here.