What is Black Cap?

Legal Definition
In English law, the black cap was worn by a judge when passing a sentence of death. Although it is called a "cap", it is not made to fit the head as a typical cap does; instead it is a simple plain square made of black fabric. It was based on Tudor Court headgear. When worn, it is placed on the head on top of the judicial wig, with one of the four corners of the black fabric facing forward.

The death penalty has now been abolished in England and Wales, but the black cap is still part of a judge's official regalia, and as such it is still carried into the High Court by each sitting judge when full ceremonial dress is called for. It is worn every year on 9 November when the new Lord Mayor of the City of London is presented to the Law Courts.
-- Wikipedia
Legal Definition
The head-dress worn by the judge in pronouncing the sentence of death. It is part of the judicial full dress, and is worn by the judges on occasions of especial state. Wharton.
-- Black's Law Dictionary