"Snape's Head of Slytherin House. They say he always favors them -- we'll be able to see if it's true."
"Wish McGonagall favored us. "
-- Ron and Harry (PS8)
Each of the four Hogwarts Houses has a Head, a staff member who is responsible for the students in that house.
During Harry’s years at Hogwarts, the Heads were:
Slytherin – Severus Snape
Gryffindor – Minerva McGonagall
Ravenclaw – Filius Flitwick
Hufflepuff – Pomona Sprout
In what would have been Harry’s seventh year, Snape became Headmaster following the death of Dumbledore, so Horace Slughorn replaced him as Head of Slytherin, a job Slughorn had held previously from the 1940s – 1981 (HBP4, DH30).
Like the Hogwarts ghosts, each Head of House was also a member of that house when they were at Hogwarts (JKR). Perhaps because they share a common background with the students in their respective houses, Heads often encourage, rather than discourage, house pride and rivalry. The competition surrounding Quidditch was legendary between Minerva McGonagall as Head of Gryffindor, and Severus Snape as Head of Slytherin.
In spite of the rivalry, the Heads usually worked together without drama or arguments. Snape and McGonagall usually agreed on the use of detentions, although it often seemed as if they played favorites, and let their own students off more lightly.
While the Heads of Houses dealt with the problems of various children, they mostly left the children on their own and did not mingle much in the various common rooms unless there is an emergency. When Hermione Granger and Penelope Clearwater were petrified by the Basilisk, McGonagall said: "All students are to make their way back to the House common rooms, where their Heads of Houses will give them further information" (CS14). McGonagall entered the Gryffindor common room just once for that announcement in second year, and she did not enter again until a year later when Harry received a Firebolt for Christmas and she took it away to have it tested before he tried flying on it (PA11).
The Heads were totally loyal to Dumbledore, especially when he was usurped and sacked by by Dolores Umbridge in Harry's fifth year. Flitwick pretended he was unable to clean up the Weasley Twins' swamp (OP29), McGonagall encouraged Peeves to unscrew a crystal chandelier (OP30), Snape created fake Veritaserum for her (OP32), and Sprout awarded Gryffindor 20 points in honor of the Quibbler article about Harry standing up to the Ministry (OP26).