The generic term 'Counselling' was coined by the American Clinical Psychologist, Carl Rogers, who founded the Person-Centred approach to therapy. It is the basic set of perspectives, techniques and procedures that are certainly necessary for the building of an effective therapeutic relationship. I would say that they are present in any effective therapy, across the vast majority of models and modalities.
Rogers asserted in "On Becoming a Person", that there were three core and "necessary and sufficient conditions", for effective therapy. Unconditional Positive Regard, Empathy and Congruence/Authenticity.
This is usually the first model of therapeutic practice that Counsellors are trained in and which often remains their core model. It is so deceptively straight-forward, it's easy to teach, but isn't so easy to practice, in that the therapist has no agenda whatsoever other than to follow non-judgementally wherever the client might lead, and to offer the core conditions. They are the three mentioned above which Rogers thought were both "necessary and sufficient" for people to grow in their own way. He described therapy as a journey from a place where someone is limited by their own self-created obstacles to growth, towards another experience of themselves, which he called becoming a "fully-functioning person".
Typically this approach is
open-ended, the client decides how long to stay
unstructured, the client brings whatever he/she wishes and the therapist will not impose any agenda
undemanding of the client's time between sessions, so no homework tasks
BE AWARE anyone can legally call themselves a counsellor if they have passed some form of training. Trainings vary greatly in quality and can vary from a ten week course to a 3 or 4 year degree programme. Sometimes graduates may take postgraduate 1 to 2 year trainings in counselling which usually confers an Advanced Diploma or a Post-Graduate Certificate in Counselling. The professional body for Counsellors is the British Association for Counselling and Psychotherapy. If a person is just a member of the body they may have very little training, they can be members without being qualified. If they are an accredited member, they will have had three years experience post qualifying and would have submitted some work for accreditation.