When Hogwarts was founded, each founder had a wildly different idea of what the future of Wizardkind should look like and should be. This disagreement led to the foundation of the House system. Each founder had an idea of the kind of student they wanted to teach.
Salazar Slytherin believed that magic should be kept within all-magic families; he is known for his distrust of Muggle-born students, and believed that they should not be admitted into the school. Slytherin handpicked his students, and paid particular attention to the qualities he valued—he wanted to teach students who were resourceful and clever, cunning and ambitious. He valued blood purity, a disregard for rules, and also selected students who, like him, were skilled in speaking Parseltongue, the language of snakes (the emblem of Slytherin house). It is believed that those who can speak Parseltongue are in some way related to or descendent from Salazar Slytherin. After his falling out with Godric Gryffindor—and the rest of the founders siding with Gryffindor—Slytherin built the Chamber of Secrets, which housed a Basilisk that Salazar intended for his heir to use to purge Hogwarts of Muggle-borns.
Rowena Ravenclaw is the person credited with the location and name of Hogwarts, which she chose after a dream she had that showed her both a warty hog and a cliff overlooking a lake. It was also Rowena who devised the Hogwarts floor plan—a floor plan that moves and changes like a living being. Ravenclaw was known as the best witch of her age. Her ideal student was creative and clever, with a sharp mind and wit. Ravenclaw disagreed with Slytherin about the value of Muggle-born students, and in fact, many students in Ravenclaw house were actually Muggle-born. She was the original owner of the Diadem of Ravenclaw, which was said to enhance the wearer’s own wisdom.
Godric Gryffindor was known as the best duelist of his age. Gryffindor valued courage and bravery, and picked students that he believed were capable of bold, heroic deeds. He was the founder most in favor of admitting Muggle-borns into Hogwarts, which became a major factor in the splitting of Slytherin from the school. Gryffindor is also the source of the Sorting Hat—when the founders realized there would be no method in place to continue sorting students into the four houses after they died, Gryffindor took off his own hat. The four founders enchanted the hat so that even after they died, the hat would act as a kind of representative and sort students according to their own values.
Helga Hufflepuff chose her students based not on blood purity or any specific traits such as ambition or intelligence. Helga Hufflepuff accepted students of all kinds, including Muggle-borns. Hufflepuff chose students who valued fairness and loyalty, and who were willing to work hard to gain their success. Helga took the students that the other founders would not, and brought them together, teaching them all everything she knew. She also treated them all equally and fairly. Hufflepuff is the one credited with bringing house-elves to work at Hogwarts, where they would not be subjected to the cruelty and abuse that is common among high-class pureblood households who employ house-elves. Helga’s recipes are also the basis of many of the staple foods seen and eaten at Hogwarts feasts—and many of those recipes are still in use.
Each founder had a vision for Hogwarts, and through the House system, each of those visions came to life. Even after death, the four founders of Hogwarts shape the world and the future. While Hogwarts may be their collective legacies, each house stands as evidence of each Founder’s individual impact on Wizarding society.