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 are:
Borneal - found in cinnamon and wormwood is said to have a calming effect. Used for recovery from fatigue, illness and stress.
Caryophyllene - found in black pepper, clove and cotton and is said to be an anti-inflammatory and analgesic.
Cineole/Eucalyptol - found in rosemary and eucalyptus is said to increase circulation, reduce pain and centers/balances.
Delta 3 Carene - found in rosemary, pine and cedar resin and is said to dry excess fluids: tears, sweat, runny noses and excess menstrual flow.
Limonene - found in citrus fruit, rosemary, juniper and peppermint and is said to be an anti-fungal and anti-cancer agent.
Linolool - found in lily and citrus and is said to possess anti-anxiety attributes and is a sedative.
Myrcene - found in marijuana, mangoes, hops, lemon grass, verbena and mercia. It is said to possess antimicrobial, antiseptic, analgesic, antioxidant, anticarcinogenic, antidepressant, anti-inflammatory and muscular relaxing effects.
Pinene - found in rosemary, sage and eucalyptus and is said to increase mental focus and energy, and functions as an expectorant and a bronchodilator, and topical antiseptic.
Sabinene - found in oak trees, tea tree oil, black pepper and carrot seed oil and is said to be an effective antioxidant.
Terpineol - 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.