Dark green, delicate and aromatic, curry leaves are, as you'd expect from their name, an ingredient used in Indian curries, at least in certain parts of the country. Their use is not limited to curry, though, or to Indian cuisine - they're also used in countries such as Sri Lanka and Indonesia. The distinctive smell and flavour of the leaves are strongest when they're fresh; when dry, they become brittle, and the flavour and aroma fade.
According to Monisha Bharadwaj's book The Indian Kitchen, curry leaves play an important role in ayurvedic medicine, where they're used to treat conditions as wide ranging as diabetes, digestive disorders and premature greying of the hair.
Curry leaves are usually sizzled in oil at the start of the cooking process, so their flavour can add depth to long-cooked dishes. Bharadwaj uses them in a dish of batata vada - another name for aloo bonda, a recipe for which I gave in Post Magazine several weeks ago. Although she adds asafetida and garlic, our recipes are quite similar: the boiled potatoes are combined with flavourings such as turmeric and fresh chilli, then mixed with mustard seeds that have been heated in oil with cumin seeds and curry leaves. The mixture is shaped into balls, dipped into a chickpea flour batter, then deep fried.