The Fountain of Magical Brethren consists of a huge gold statue at the Ministry of Magic depicting a witch, a wizard, a centaur, a goblin, and a house-elf. Though the statue is impressive, Harry notices almost immediately that the depictions of the non-human creatures are decidedly problematic: the centaur and the goblin look at the humans adoringly, something that, in Harry's experience, real centaurs and goblins would never do. This suggests that the fountain represents Fudge and the Ministry's vision of an idealized world, one in which wizards reign supreme and non-human creatures accept the Ministry's authority and their own subjugation without question. As disturbing as these portrayals are, it's also important to note what beings the ministry leaves out--namely, merpeople, giants, and "half-breeds" like werewolves--as this suggests that in the Ministry's eyes, those beings will never be accepted members of society or receive any rights. This again casts the fountain as one that visually represents Fudge's agenda for who's included in society and who isn't.
When Dumbledore animates the figures in the fountain and uses them to protect Harry from Voldemort, he symbolically destroys Fudge's narrow and discriminatory vision of the future and suggests that non-human beings are important and should be brought into the fold, as this is the only way that the side of good will be able to defeat Voldemort in the coming showdown. Further, destroying the fountain altogether leaves room for the Ministry to create a new fountain that symbolizes a better, more equal world and gives non-human beings the respect and dignity they deserve.
The Fountain of Magical Brethren Quotes in Harry Potter and the Order of the Phoenix
"Sirius did not hate Kreacher," said Dumbledore. "He regarded him as a servant unworthy of much interest or notice. Indifference and neglect often do much more damage than outright dislike...the fountain we destroyed tonight told a lie. We wizards have mistreated and abused our fellows for too long, and we are now reaping our reward."