Essential oil of Peppermint generally comes in one of three forms: natural, redistilled, triple distilled. There are other variations, but these are the three basic categories. The term natural is a bit confusing, because it seems to suggest that the redistilled and triple distilled are unnatural, which is incorrect. They have simply been steam distilled a second and third time respectively.
It would be better to describe these as: first distillation, second distillation and third distillation. The natural, or single distilled, peppermint is characterized by a rather green, herby aroma- much like you would expect a freshly crushed peppermint leaf to possess. With each progressive distillation the oil becomes less herbaceous and more intense, sweet and candy-like. It is redistilled and triple distilled peppermint oil that is going to be found in more personal care and cosmetic applications, as it has a much crisper, cleaner aroma that the first distillation.
Please note: Peppermint is considered a dermal irritant - avoid application of known dermal irritant essential oils on any inflammatory or allergic skin condition; avoid undiluted application; avoid application on open or damaged skin; and dilute known dermal irritants with appropriate vegetable oil or other carrier. When using an essential oil you have never used before, perform a skin patch test. For external use only.