Wikipedia.) It's a polyphenol, meaning it has a phenyl ring (the six sided molecule) and and has a hydroxyl group (the OH and the -ol in the name). It's part of a group of compounds called phenylpropenes, which also include chavicol, estragole, and safrole. These other phenylpropenes are known to be carcinogenic and toxic in various ways, and eugenol can be hepatoxic (toxic to your liver) at higher doses (click here).
As an aside, when you're doing a search for safrole, you'll find a lot of sites about making MDMA or ecstasy as it is apparently a major component of the process.
Eugenol is known to have anti-oxidant properties (Antioxidant activity of eugenol: a structure-activity relationship study, Gülçin İ, Journal Of Medicinal Food; 2011 Sep, p 975) and has shown itself to be a good anesthetic in rats (as per this study). It is used as an anti-inflammatory (click here), anti-oxidant, analgesic, and penetration enhancer in medical products (Eugenol: a natural compound with versatile pharmacological actions. Pramod K, et al. Natural Product Communications;2010 Dec, p 1999). It is showing promise as an anti-microbial - "...eugenol above 200 ppm completely inhibited mold growth" (click here for abstract).
Eugenol can be an allergen and skin irritant. (If you want to know more about this, click here for a really long PDF on eugenol). Think carefully about using eugenol containing essential oils in products for someone with sensitive or allergic skin.