Curry leaves belong to the curry tree, a tropical tree native to India and Sri Lanka. It produces small highly aromatic leaves that are used in a lot of Indian curries common to Western and Southern India.
Typically used fresh, the leaves have a very short shelf-life after being removed from the tree. The leaves are also rich in iron. Although the name evokes images of 'CURRY' the flavor of curry leaves is quite unique and does not match traditional curry powders that most people identify with curry.
Traditionally, curry leaves are toasted in oil before any other ingredients are added. I added them to a broth lined pan instead of oil and the whole house smells like divine. As the leaves cook into the dish, they infuse volatile oils and aromas into the dish. Once done, the leaves can be removed although eating a leaf or two will not harm anyone. To preserve, separate each batch of 4-6 leaves (that's the amount used per dish) between folds of paper towel or parchment paper and freeze in a zip-lock bag. Unlike some of the more tender herbs, curry leaves maintain their texture and flavor really well in the freezer and you won't be able to tell the difference between fresh and frozen leaves.
They can be used dry however, the aroma is largely lost with drying. The leaves have a long history in traditional Indian medicine (Ayurveda). They are valued for their anti-diabetic, antioxidant, antimicrobial, anti-inflammatory and hepatoprotective, and anti-hypercholesterolemic qualities. Interestingly, a study was published in 2001 showing that Girinimbine - one of the many alkaloids found in curry leaves - inhibits growth and actually promotes cell death in human hepatic carcinoma cells (in culture!) ... so eat away!!