Curry leaves are the leaves of a small tree, native to India. Though they may be used in curries, confusingly, they are not normally an ingredient of curry powder.
Its leaves are highly aromatic and are used as a herb. Their form is small and narrow and they somewhat resemble the leaves of the Neem tree.
They are commonly used as seasoning in Indian and Sri Lankan cooking, much like bay leaves and especially in curries with fish or coconut milk. In their fresh form, they have a short shelf life though they may be stored in a freezer for quite some time,though they lose much of flavour. They are also available dried, though the aroma is inferior.
I have not been able to buy fresh curry leaves in the UK as most of what was sold as fresh was already dried out!