Both cilantro and coriander are derived from the coriander plant. However, cilantro is specifically the leaf of the plant, whereas coriander refers to the plant's seeds. Despite being products of the same plant, cilantro and coriander have very different tastes.
To most people, cilantro has a sharp, acidic taste, reminiscient of citrus. However, some people find the aroma to be rancid and the taste soapy, making them very averse to the herb. It is a common ingredient in salsas and guacamoles, as well as many Middle Eastern, Indian and Mexican dishes.
Coriander has an earthy and floral flavor, though still with a hint of citrus. It's used predominantly in heavily spiced foods, such as sausages and curry. The essential oil from the seed is used to flavor some alcohol and tobacco products.