The active compounds of essential oils are the hydrocarbons founds in plants.
These are made up almost exclusively of terpenes (monoterpenes, sesquiterpenes, diterpenes). There are also oxygenated compounds which are mainly esters, aldehydes, ketones, alcohols, phenols, and oxides.
There are three types of molecules in essential oils that do the bulk of the work on and in our bodies; phenols, sesquiterpenes, and monoterpenes.
I could get into more detail here, but I will leave to the chemists and scientists!
For more detailed research explaining the science, check out the book Molecules of Emotion: The Science behind Mind-Body Medicine, by Candace Pert
Suffice to say, it is fascinating stuff! I am constantly amazed how well essential oils work in the body.