What is a Aromatherapist and what kind of training do they receive?

A Aromatherapist is someone who has been formally trained in the use of essential oils, essential oil safety, history of essential oils, the distillation processes, blending, dilution rates, contraindications etc., and has a basic understanding of anatomy and a familiarity with plants/individual oil makeup (chemical constituents and their efficacy/therapeutic effect).  A aromatherapist is always working toward a whole body balancing - meaning, they are looking at health as a balance of healthy eating habits, routine exercise, good sleep habits, supplements, etc. and also, always considering the role of our spiritual and mental well being in that balancing act.   Essential oils and aromatherapy can play a part in bringing the body back into balance and while aromatherapy is not a licensed modality at this time in the USA, it may be, in the near future, as we become more and more aware of the benefits (with virtually no side effects if used according to standard dilution rates/recommended daily dosages) natural, pure essential oils can bring.
Here is a article that states more specifically what a Aromatherapist can/cannot do according to a accredited school - American College of Healthcare Sciences: What Can I Legally Do As An Herbalist, Aromatherapist, Or Other Holistic Health Practitioner?
Not all aromatherapy training/education is the same.  If you are looking for a certification in aromatherapy or to become a Registered Aromatherapist be sure to do your homework before entering into a program.  Some can run a small fee of $300 for a weekend course and some upwards of $5000+ for a accredited certificate or diploma program.  Course are even available online.  To some degree, you get what you pay for.  If you are simply looking for some basic training so you feel comfortable using essential oils at home for you and your family, a weekend course or 16-20 hours of training is a great place to start.  However, if you are seeking to enhance your current holistic practice with a specialty like aromatherapy a more intensive course might be a better fit.   Training you might receive in the United States will also vary from what may be available/offered in other countries.