An explanation from an Episcopal priest:
I saw somewhere on Facebook where a priest asked the following: “What exactly is the point of a biretta.” At last count there were 41 responses, ranging from indignation to clergy humor. I actually liked the question – what is the point of a biretta.
From a practical standpoint, I can’t think of one. It doesn’t do anything, doesn’t protect my head from anything, doesn’t even have any real theological symbolism, at least not to my knowledge. But I wear it the same reason a policeman wears a badge. I wear it the same reason a doctor’s coat hangs near the knee. I wear it for the same reason a pilot wears his hat. None of these serve any real practical purpose. Sure its helps with identification but any number of things can identify. Policemen don’t need badges, doctors don’t need white coats and pilots certainly don’t need a hat – but that’s what policemen, doctors, and pilots wear. That’s who they are.
Priests, at least some of us, wear birettas. No one else does. Just clergy. If you see a strange hat with three or four blades and a pom pom tuft, there is no doubt who wears it. In a time where boundaries are blurred and identities are confused, the biretta – that silly little hat – makes a statement: I’m not trying to fit in. I’m not trying to be cool. I’m a priest. Because trust me, no one thinks they look sharp in a biretta. We may joke and deny this, but we know how we look, and we really don’t care. We’re priests and it’s not about us.
There’s a wonderfully obscure verse in Exodus 28.40 and it’s in reference to the vestments of Aaron and his priestly descendants “And for Aaron’s you shall make coats and girdles and caps, you shall make them for glory and beauty.”
That’s their purpose – to stand for the unique purpose of pointing the glory of God and to be used in acts of profound beauty. They’re not a style I would have created. But it’s not for my glory. When you see a biretta, you know it’s for worship. When you see a biretta, you know it’s for a priest. I think we as priests need to remember that too.