Essential oils are highly concentrated aromatic extracts which are distilled from a variety of aromatic plant material including grasses, leaves, flowers, needles & twigs, peel of fruit, wood and roots.
I have used them for years for a variety of things. I use them to treat sinus conditions and headaches. And I've used them to relax my children at bedtime when they were younger (put lavender on a pillow case).
Here are some popular oils and their uses as ranked by the National Association for Holistic Aromatherapy
Peppermint -- Useful in treating headaches, muscle aches, digestive disorders such as slow digestion, indigestion and flatulence
Eucalyptus -- Helpful in treating respiratory problems, such as coughs, colds, and asthma. Also helps to boost the immune system and relieve muscle tension
Ylang Ylang -- Helps one to relax, and can reduce muscle tension. Good antidepressant
Geranium -- Helps to balance hormones in women, good for balancing the skin. Can be both relaxing and uplifting, as well as antidepressant.
Lavender -- Relaxing, and also useful in treating wounds, burns, skin care