In Harry Potter and the Half-Blood Prince, Horace Slughorn teaches Potions.
Slughorn returns to Hogwarts as the Potions professor after Severus Snape takes the Defence Against the Dark Arts post. Harry initially expects to study another subject, but he receives an old Potions textbook containing handwritten notes that help him excel in class.
The textbook once belonged to Snape, whose annotations include the spell Sectumsempra. Harry's academic success with it helps Slughorn notice him and eventually give him a private memory about Tom Riddle. That memory is essential to Dumbledore's investigation of Voldemort's Horcruxes.
The subject has a complicated teaching history in the films. Snape teaches Potions in the earlier school years, while Slughorn returns specifically to fill that role in Half-Blood Prince. Slughorn is played by Jim Broadbent, and the film also shows his famous “Slug Club” gatherings.