A composite emblem. Its primary meaning is purity and chastity - the foundation being of fine linen. The gold band denotes supremacy. The first cap of dignity was adopted by Pope Damasus II. in 1048. The cap was surmounted with a high coronet in 1295 by Boniface VIII The second coronet was added in 1335 by Benedict XII., to indicate the prerogatives of spiritual and temporal power combined in the Papacy. The third coronet is indicative of the Trinity, but it is not known who first adopted it; some say Urban V., others John XXII., John XXIII., or Benedict XII.
“The symbol of my threefold dignity, in heaven, upon earth, and in purgatory.” —Pope Pius IX. (1871).
The triple crown most likely was in imitation of that of the Jewish high priest.
“On his head was a white turban, and over this a second striped with dark blue. On his forehead he wore a plate of gold, on which the name of Jehovah was inscribed. And, being at once high priest and prince, this was connected with a triple crown on the temples and back of the head.” —Eldad the Pilgrim, chap. x.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894