Reactance refers to when people attempt to restore the freedom by directly contradicting the rule that threatened their freedom.
In the lecture, the professor gives two examples.
First, a kid likes to play in a playground. One day, his parents don't allow him to play there anymore, for no apparent reasons. The kid would feel it's unfair and want to play there even more. And he would sneak over there despite the parents' rule.
Second, a town banned selling a kind of soap. Because one of its ingredients was harmful to the environment. But people thought it had nothing to do with its ability to clean things. People just felt upset and it was not right. Therefore, one week before the law went into effect, people went to buy more lots of this soap, way more than they would other circumstances.