Like many of the "new age" alternative healing methods, aromatherapy has its roots in ancient history. The ancient Greeks and Egyptians used essential oils in perfumery, massage and in aromatherapy, although that may not have been what they called it back then.
The human body absorbs the benefit from essential oils in various ways, not just by inhaling, but also through massage. The constituents of the oils interact with various parts of the brain, stimulating, exciting, soothing, or calming, as they are designed, resulting in an overall healthier person.