These are most often encountered in the context of the United States Military-Industrial Complex, and Intelligence Agencies, such as the CIA

In the United States, the Federal Budget must, in theory, be debated by the United States Congress, before a proposed budget is sent to the President for his signature. This was to allow Senators, Members of the House and the President to call out abusive, corrupt or unnecessary expenditures. It made creating the national budget a relatively public and open affair, inviting many eyes into the process for oversight. Obviously this could not be allowed to continue.

However, in a nation that is at war - the information of how much is being spent on what military activities can be of crucial importance. Denying the enemy this information came to be considered important. Denying the public this information was more important.

The solution was to pick a very small group of Senators and Representatives, of extremely carefully vetted trustworthiness, and show them the the full budget - while everyone else would get a copy where the sensitive information had been blacked out. The trusted senators could then advise their colleagues to vote yes or no on the unseen items. Yes--if they wanted their pork passed too.

There some deeply silly effects from set-ups like this. For instance a Congressman may see something corrupt or unlawful - and be prevented from speaking out or reporting this - because that would violate his security clearance.

The other silly thing is that some of these Black items on the budget are general. "operations" and so on. These black budget allocations of taxpayer money can be diverted and hidden yet further from any oversight that might get the hiders in hot water.

In some cases the funds go to good and necessary uses, like Bureau-13, other times funds are used for destructive uses, like The Shop. Most of the time it is simply a way to get what you are really doing off the record in the interest of national security so you can keep doing it without oversight.