Cilantro is the leaves of the coriander (Coriandrum sativum), a small, delicate plant that is native to southern Europe, North Africa, and parts of Asia. Coriander is interesting because three distinct parts of the plant are used culinarily, and they have three distinct flavors.
The fruits (seeds) are sharply flowery-lemony and green, almost like lemongrass without the citrus. They have high concentrations of pinene and linalool.
The roots (which are uncommon in the United States but are popular in Thai and Malaysian cooking) have a deeper, earthy note and a spicy greenness.
The leaves (what we know as cilantro) are polarizing. Some people sense them as rich, musky and warmly grassy. Others think they smell of soap and vomit and detest them. This is due to a class of aroma chemicals called aldehydes, which are chained hydrocarbons -- think of the powdery/soapy aroma of Chanel #5 -- that's aldehydes. In fact, one of the tests for being a supertaster involves the smell of cilantro.
Cilantro is important in a wide range of cooking styles, but especially Mexican, Indian, Thai, and Vietnamese. The aroma and flavor of the leaves is delicate, so cilantro is typically used as a garnish, or stirred into curries at the last second.