The essential oils are the part of the plant that possesses the fragrance of the plant or flower in concentrated form.
Essential oils are like the name suggests - oily compounds. When the plant material is chopped up and put into a container and steam is passed through it, the oils are extracted from the plant material. Once the steam cools down the there will be the plant material and a solution. When the solution has cooled, you will notice that it looks like a mixture of oil and water. It is. When the water cooled from steam the oil is no longer "mixed" with the steam. The oil can now be separated (using an industrial process) from the water giving a pure oil product with the smell of that part of the plant that has been distilled. This oil is called the essential oils of that plant.
Some plants are sources of several types of essential oils since there are different parts of the plant that have different smells e.g. the flower of the tree would have a different smell from the oil from the tree itself, so the oil extracted from the fruit would be different to the oil from the flower, even though it is the same tree hence one plant could yield a variety of essential oils.
The most well-known essential oil is probably rose oil, produced from the petals of Rosa damascena and Rosa centifolia.
Man-made essential oils are not in the form seen in nature. The man-made form is a concentrated version so generally they should not be applied directly to the skin in their undiluted or "neat" form when bought in a bottle. Some can cause severe irritation, or provoke an allergic reaction. Instead, essential oils should be blended with a vegetable-based "carrier" oil before being applied.
While some advocate the ingestion of essential oils for therapeutic purposes, medical advice should be sought. Some common essential oils such as Eucalyptus are toxic internally.