Curry leaves are the shiny, dark green, aromatic leaves of a tree from the citrus fruit family that release a deliciously nutty aroma when fried in hot oil. A staple of South Indian cooking, curry leaves are used in Indian and South East Asian cuisine in the same way as bay leaves are used in the West. staple of South Indian cooking, curry leaves are used in Indian and South East Asian cuisine in the same way as bay leaves are used in the West.