Mostly it's for professional recognition. It is a way of saying "I am qualified and have achieved that qualification through a reputable source". This is important in the eyes of potential clients who don't know anything about you!
Health care rebates - health funds need to know that they are paying out money for a therapist who is qualified to do the work that they say they do. Some bodies such as ATMS and ANTA create a link with most health funds so that you don't have to.
Insurance deals - always a goodie! Most professional bodies have an alliance with an Insurer.
The professional body represents its members in parliament and may have influence in creating health policies which will benefit you and your clients.
Provide CPE events regularly which make it easy to gain that continuous education.
To form networks with other professionals in your industry.
Which one should I go with? Well, it depends on your chosen profession and your own preferences.
Some people like to join a body which covers a broad range of therapies (particularly if your training covers a range of therapies) and others will like to just join their professions body. You can always join more than one.
I suggest that you do your research and pick a body which aligns with your values and which you feel will represent you and your chosen profession well.
Associations that cover a broad spectrum of therapies:
Australian Traditional Medicine Society (will link to most health funds for you)
Australian Health Professional Regulation Agency - AHPRA
Australian Natural Therapists Association
International Institute for Complementary Therapists
Some of the bodies which provide services to a particular field:
Australasian Acupuncture & Chinese Medicine Association
Chiropractors Association of Australia
Australian Counselling Association
Australasian Podiatry Council
Australian Registrar of Naturopaths and Herbalists
Australian Association Massage Therapists
Australian Kinesiology Association
Australian Homeopathic Association
of course there are many more for each of our specialities.