At least some content in this article is derived from information featured in Fantastic Beasts: The Crimes of Grindelwald. As such, spoilers will be present within the article.
Your point about Wizard dominance being FOR THE MUGGLE'S OWN GOOD -- this, I think, is the crucial point. Yes, we have been given power and yes, that power gives us the right to rule, but it also gives us responsibilities over the ruled. We must stress this point, it will be the foundation stone upon which we build. Where we are opposed, as we surely will be, this must be the basis of all our counterarguments. We seize control FOR THE GREATER GOOD. And from this it follows that where we meet resistance, we must use only the force that is necessary and no more. (This was your mistake at Durmstrang! But I do not complain, because if you had not been expelled, we would never have met.)
- —One of Albus Dumbledore's letters to Gellert Grindelwald in their school years as they plotted Muggle domination.[src]
"For the Greater Good" (German: "Für das Größere Wohl") is a phrase that Gellert Grindelwald used to justify his horrific actions in the 1940s global wizarding war and it was engraved over the entrance of Nurmengard, the prison he constructed to house those who opposed him. It expressed his belief that what he was doing was to be of eventual benefit to everyone, but that a small number of people would have to suffer to bring these benefits about.
History of the phrase
When Grindelwald visited Godric's Hollow in the 1890s, he struck up a friendship with the young Albus Dumbledore and told him about his plans to overthrow the International Statute of Wizarding Secrecy and establish a regime in which wizards were placed above Muggles. Within these talks, Grindelwald said that the regime would be for the Muggles' own good and Dumbledore wrote a letter in which he said:
"Yes, we [wizards] have been given power and, yes, that gives us the right to rule, but it also gives us responsibilities over the ruled... We seize control for the greater good. And from this it follows that...we must use only the force that is necessary and no more."
After Dumbledore severed ties with Grindelwald following a duel that claimed the life of his younger sister, the motto became Grindelwald's alone. It became the rallying cry for his revolution that would allow him to bring the wizards out of hiding. Following the First World War, a destructive Muggle conflict during which several wizards fought on both sides (despite the official neutrality of magical governments), Grindewald emerged to preach his message of wizarding domination to the world, arguing that the barbaric actions of the Muggles could have been prevented had the wizards ruled over them. Followers joined Grindelwald's cause and launched attacks all across Europe. Despite a brief disappearance followed by his arrest during the Obscurus attack on New York in 1926, Grindelwald escaped and continued to propagate his message.
Although Grindelwald was seen as the most powerful dark wizard in the world, Grindelwald and his followers knew that there existed only one person in the wizarding world with the capability to challenge him: Albus Dumbledore, his old friend who had once embraced their philosophy. Thanks to their Blood pact, Dumbledore was rendered incapable of facing Grindelwald but Grindelwald knew better than to assume Dumbledore would just let his crusade go unchallenged and as attempting to kill Dumbledore personally was impossible as the pact also prevented Grindelwald from fighting Dumbledore, making it a double-edged sword to the Greater Good revolution. Grindelwald's search for the Obscurial Credence Barebone was motivated by the belief that he, as a pure magical force capable of incredible destruction, would be able to destroy Dumbledore in his place.
Grindelwald's 'For the Greater Good' revolution terrorized the wizarding world for two decades and had backed the governments into a corner but by 1945, fortune finally left them when Dumbledore finally destroyed the Blood Pact and was able to confront his old friend. In what was described by those who witnessed it as the greatest battle of magic ever undertaken, Dumbledore defeated Grindelwald and imprisoned him in his own prison fortress of Nurmengard, ending the idea of the domination of wizards over the world.
However, despite his participation in Grindelwald's defeat and having rejected Grindelwald's cause, during the uprising of Lord Voldemort, Dumbledore would show himself to still belief in the term he had coined for his former best friend, but unlike Grindelwald, his approach towards it was much more benign.
Behind the scenes
- Ironically, Elphias Doge's tribute to Dumbledore in the Daily Prophet, "Albus Dumbledore Remembered", stated of Dumbledore that "He died as he lived: working always for the greater good..."
- "The greater good" is an essential idea of the utilitarian philosophy. "For The Greater Good" may also be a reference to "Arbeit macht frei" (German, "Work makes [one] free" or "Work liberates") the motto that was mendaciously inscribed over the entrance gates to several Nazi concentration camps (The exact wording of the inscription at Nurmengard is unknown, since Grindelwald's exact nationality or his language of preference, are not specified in the books: the German translation of his slogan would be "Für das höhere Wohl", although the official German translation in the book reads "für das größere Wohl").
- Harry Potter and the Deathly Hallows (First appearance)
- Fantastic Beasts and Where to Find Them: The Original Screenplay 
- Fantastic Beasts and Where to Find Them (film) (Mentioned only)
- Fantastic Beasts: The Crimes of Grindelwald - The Original Screenplay
- Fantastic Beasts: The Crimes of Grindelwald