Peppermint (Mentha piperita) is a plant which is a hybrid from watermint and spearmint, used initially for culinary and food manufacturing purposes but has also been used for its supposed medicinal benefits. Peppermint has an oil component which appears to be its medicinal component, and this oil has a very large content of menthol which is seen as its bioactive ingredient. This menthol is nontoxic at the recommended dose, but is the same menthol also found in some cigarette products.
The main medicinal role of peppermint is due to its muscle relaxing properties in the stomach and intestinal tract, and internal usage of peppermint appears to be able to speed up the early phase of digestion in the stomach while reducing colonic motility. It is known as a carminative agent (thought to relief flatulence), and it has a fair bit of evidence to supports its usage in reducing abdominal pain in persons with irritable bowel syndrome (IBS). It doesn't seem to influence other symptoms of IBS too much, but the reduction of abdominal pain is quite notable.
Other possible benefits of peppermint oil include fast headache relief (which involves applying a topical solution of 10% peppermint oil to the scalp at the onset of a tension headache) and possibly a reduction in nausea when used as aromatherapy. It is safe with the recommended dosages, but overconsumption of peppermint oil supplements does have a toxic level which is feasible to reach intentionally.