What is an inquisition?
The best way to explain it is to imagine some examples.
In a Hospital
Imagine a hospital where the majority of health workers are very, very devoted people. They work long and hard to alleviate suffering and to cure patients of their diseases, and all this for often meager wages.
Now suppose that a minority of health workers in that hospital were in fact serial killers, and that every morning, some patients would be found dead, strangled in their beds.
The Director of that hospital would have to start up some kind of inquiry to flush out the minority of bad health workers, and then deal with them according to the law.
Since this would be in a hospital setting, we wouldn't call it an "inquisition", but basically it's the same thing.
In a School
Imagine a school where the majority of teachers are very kind and competent people, and are paid even less than in the aforementionned hospital!
Suppose now that a minority of teachers disseminated hate propaganda in that school, for example that homosexual women according to the Bible are "possessed by the Devil and despised by God", or some other moronic thing. Of course, if these teachers acted in the open, there wouldn't be an issue. But imagine that this minority of bad teachers avoided spreading their propaganda in the presence of the Principal, the parents or the good teachers.
The Principal of that school, after receiving complaints from parents, would have to set up some sort of investigation. Since we suppose that the bad minority is doing everything it can to hide itself inside the good majority, the Principal of that school would have to find a way to flush out these people. A method he could use could be to gather everybody in the Gym (teachers and students), and then clearly explain why homosexual women are human beings like you and I, that they have the same rights, and so on. The Principal could then call upon all teachers, one after the other, to come to the microphone to assert their support for what he said. The Principal could then finish up by asking all the students to report to him immediately any type of offense against the rights of homosexual persons.
This wouldn't necessarily solve the problem in that school, but according to us, it would be a step in the right direction. Moreover, if the Principal had been misinformed (and that in fact there were no bad teachers in that school), the worst that could happen is that everybody would get a reminder of some important information, which is worth repeating once in a while anyway.
Other Examples
You can consider the audits done in companies by independant accountants, or the Quality Assurance Department in a manufacturing plant, and even the human body. Macrophages, the largest phagocytic cells, constantly patrol the human body, looking for microbes ((Biology, 6th Ed., p. 902, by Cambell and Reece). In other words, there is a kind of "permanent inquisition" going on in our own body.
In fact, you could say that any institution (as well as any living organism) which ceases to actively fight against harmful elements which are, or could be in it, quickly dies off.