A Hate Potion is a potion which reveals the worst traits and habits of a particular person to the drinker.
The Hate Potion was recommended by the Daily Prophet's advice column for witches and wizards who are emotionally attached to a person who does not return their feelings. Although not guaranteed for a person to completely lose their feelings for a loved one, it does show the drinker the person's worst traits and habits, and so discourages them from creating a relationship with that person.
The Hate Potion's opposite is the Love Potion, as the Love Potion can undo the Hate Potion's effects.