Wiktionary
koilonychia
n. A deformity of the nails characterized by concavity of the outer surface
Wikipedia
Koilonychia
Koilonychia (from the Greek: koilos-, hollow, onikh-, nail), also known as spoon nails, is a nail disease that can be a sign of hypochromic anemia, especially iron-deficiency anemia. " It refers to abnormally thin nails (usually of the hand) which have lost their convexity, becoming flat or even concave in shape. In a sense, koilonychia is the opposite of nail clubbing. In early stages nails may be brittle and chip or break easily.
Koilonychia is associated with Plummer-Vinson syndrome and iron deficiency anemia.