Slay The Spire is filled to the brim with various relics both active and passive, which all serve some sort of function in one's playable deck. As players progress through the titular Spire, they'll gather a variety of these items in a variety of ways, and while most can be found at random, Cultist Headpiece cannot.
Slay The Spire Cultist Headpiece is not a very useful item either, mind. It does have its niche uses and can be employed in practical terms, but this isn't something you should rely on. Instead, consider it a vanity item, and save yourself the disappointment.
In order to get a Cultist Headpiece all of your very own, first you're going to have to roll the dice and encounter the Face Trader event as you climb the Spire. This character will offer to give you a mask you can choose for yourself, but since they don't always bring the entirety of their possible stock, the spawning of a Cultist Headpiece adds another layer of RNG.
Now, Cultist Headpiece is going to be familiar to virtually all players of Slay The Spire, as that's the "mask" thing worn by bird cultists from the start of the game. Finally getting one of your very own provides the following effect: "This relic makes your character scream "CAW! CAAAW" at the start of each battle."
And that's it, yes. Granted, it is quite funny to see your own character succumb to the Cult, but you're usually going to be able to pick a better mask from the Face Trader, so don't bother with the Cultist Headpiece unless you're doing it for the memes.