The zucchetto is the small round skullcap of the Western clergy, and among all the items of clerical dress it is the one that encodes rank with the least ambiguity.
Colour is rank
The zucchetto is worn on the crown of the head, and its colour gives the rank exactly: white for the pope, scarlet for a cardinal, amethyst or violet for a bishop, and black, where it is used at all, for a priest or deacon. There is no room for interpretation in it, and a photograph of a gathering of clergy can be read at once from the caps alone. Its name is Italian, from the word for a small gourd, describing the shape.
When it comes off
The cap is worn through much of the liturgy but is removed at the most solemn point, the canon of the Mass from the preface to the communion, in the presence of the exposed Blessed Sacrament, so that the head is bared before the consecrated host. That rule of removal is the same logic that governs the mitre, which also comes off for prayer addressed directly to God, and it marks the zucchetto as an object of ecclesiastical rank that yields, like every rank in the church, before the sacrament itself.