Terpenes are "volatile unsaturated hyrdocarbons" (read: organic compounds) found in the essential oils of plants and even some insects. Plants, such as marijuana/hemp, conifer trees and citrus trees, all which have pungent smells, are generally high in terpenes.
Okay, so they are some compound in the essential oil of pungent smelling plants, so what? Most people only really care about what benefits they can provide if they are smoked or whatever. When using pure terpene extracts, it is generally smoked or vaporized. However, since terpenes are present in most every plant that has any essential oil, there are many ways to potentially ingest a terpene.
For instance, a Mango is high in the terpene: Myrcene. And, people like to eat mangos before smoking marijuana because the myrcene can increase the effects of THC. So, if someone has a strain of marijuana that isn't very high in THC, eating a mango about an hour before smoking will cause a much 'higher' effect of the THC.
Many common Terpenes found in cannabis are:
Borneal - also found in cinnamon and wormwood is said to have a calming effect.
Caryophyllene - also found in black pepper, clove and cotton
Cineole/Eucalyptol - also found in rosemary and eucalyptus is said to centers/balances.
Delta 3 Carene - also found in rosemary, pine and cedar resin
Limonene - also found in citrus fruit, rosemary, juniper and peppermint
Linolool - also found in lily and citrus
Myrcene - also found mangoes, hops, lemon grass, verbena and mercia. It is said to possess relaxing effects.
Pinene - also found in rosemary, sage and eucalyptus and is said to increase mental focus
Sabinene - also found in oak trees, tea tree oil, black pepper and carrot seed oil and is said to be an effective antioxidant.
Terpineol - also found in flowers, citrus, apple/orange blossoms and is used in perfumes and soaps.
There are many many more terpenes and their uses and effects have not been fully documented.