"I will expect you at six o'clock on Monday evening, Potter. My office. If anybody asks, you are taking remedial Potions. Nobody who has seen you in my classes could deny you need them."
-- Severus Snape (OP24)
Snape gave Harry lessons in Occlumency, or closing his mind to invasion by the Dark Lord, under the guise of giving him Remedial Potions lessons so that Umbridge and her Inquisitorial Squad would not be suspicious (OP24). The story was believable to Draco Malfoy and others because Harry’s worst class was Potions. But of course Potions had nothing really to do with Occlumency.
- Draco did interrupt one session of Occlumency when Slytherin Quidditch player Montague was discovered stuck in a drain and Umbridge needed help from Snape to get him out. Draco appeared gleeful about Harry about taking "Remedial Potions" before leaving the room. (OP28).
- Hufflepuff Zacharias Smith also joked about Harry getting extra Potions lessons from Snape, saying "Good Lord, you must be terrible" (OP24).
- A Healer at St. Mungo's Hospital mentioned that those in the closed Janus Thickey Ward for Spell Damage such as Gilderoy Lockhart could be helped with "intensive remedial potions and charms and a bit of luck" (OP23).
Same root word as "remedy" or cure, from Latin remedialis "healing." In the educational sense, as Snape uses it for Harry, remedial means to "improve skills," with the implication that Harry was failing at Potions.
Ironically, Harry had much more trouble with Occlumency than he ever had with Potions class. The scar from the Horcrux embedded in his forehead connected him to the Dark Lord in such a way that he could not close his mind to Voldemort's activities, which is why Snape's effort failed.