mitre n.

mid-14c., "bishop's tall hat," from Old French mitre and directly from Latin mitra "headband, turban," from Greek mitra "headband, turban," earlier a belt or cloth worn under armor about the waist, perhaps from PIE root *mei- "to bind, attach" (source also of Sanskrit mitra- "friend, friendship," Old Persian Mithra-, god name; Russian mir "world, peace"). The Greek word might be borrowed from Indo-Iranian.

In pre-Christian Latin, in reference to a type of head-dress anciently worn by inhabitants of Lydia, Phrygia, and other parts of Asia Minor, "the wearing of which by men was regarded in Rome as a mark of effeminacy" [OED]. But the word was used in Vulgate to translate Hebrew micnepheth, the sacerdotal head-dress of the ancient Jewish high priests.