Wikipedia states: "An essential oil is a concentrated hydrophobic liquid containing volatile aroma compounds from plants" - what it means is that the plant material is reduced down to an "oil" (hydrophobic liquid) which readily evaporates (volatile) and which smells (usually very nice).  These "oils" carry the properties of the plant that they came from in a form that can be readily introduced to the body by smell (through the olfactory system) and through the skin (osmosis) and as with any chemical, they can have an effect on the body.

Using Essential Oils to effect the mind and the body is called Aromatherapy.