"The Inquisitor will have powers to inspect her fellow educators and make sure that they are coming up to scratch"
-- Percy Weasley (OP15)
"Good afternoon, Professor Trelawney. ...You received my note, I trust? Giving the time and date of your inspection?"
-- Umbridge (OP15)
Created the position of Hogwarts High Inquisitor.
- The Ministry gave Umbridge power to interrogate teachers during classes about subject matter and methods, as well as report to the Ministry if she wanted to give them the sack (OP15).
- Minister for Magic Cornelius Fudge also wanted to reign-in Dumbledore so he wouldn't form a student-army that might work against the Ministry, and he knew that Umbridge would be the perfect Ministry spy (OP14, OP15).
- Hermione and Harry decided to fight back by forming the very thing Fudge feared the most - Dumbledore's Army, training themselves in Defence Against the Dark Arts since Umbridge would not allow them to use their wands in class (OP16).
The Spanish Inquisition was a tribunal of the Catholic Church in 14th century Spain. The Inquisitors were charged with punishing anyone thought to be Jewish, Protestant, or merely disloyal to the throne of Spain. Sometimes there were literal witch-hunts looking for those with pagan beliefs. If someone was convicted they would be publicly tortured or burned at the stake in a mass execution known as an "auto-da-fe" (Wikipedia).
There was a Monty Python sketch titled "Nobody expected the Spanish Inquisition" making fun of sadistic Inquisitors who enjoyed torturing others or being tortured themselves. The phrase has become common in popular culture when someone feels harassed by questions or personal attacks.