Mantle in humans means a cloak or a covering while in birds it comprises of the feathers just below the nape. It forms a V-shape under the head. In some birds the mantle is the same colour as the nape and head, but in some birds the mantle is so prominent that they have become part of the birds's name.
(For example - Yellow - Mantled Weaver)
In the picture below the black area just below the orange is the mantle.
Mantle is also used as a verb. When a bird covers another bird or something else with its wings, it is called mantling. They usually do this to hide their prey from other birds.