Final answer:
Professor Snape taught Harry's class to make the Boil-Cure Potion, an introductory lesson in the magical world of Harry Potter.
Step-by-step explanation:
The first potion that Professor Snape taught Harry's class to make in the Harry Potter series was the Boil-Cure Potion. This potion is mentioned in the book "Harry Potter and the Philosopher's Stone", where it is described as an introductory potion that Snape requires his first-year students to brew. Its purpose is to cure boils, and thus it serves as a practical example of how potions can have beneficial effects in the world of Harry Potter.