In Attack on Titan, the threat of Titans is forever looming over the lives of everyone who lives behind the Walls. Some people do a better job of dealing with the stress than others. For Jean, he copes by covering his ears. He tends to do this whenever he gets overwhelmed, which is, understandably, all the time. For example, he did this when Sasha died.

In fact, in Jean’s quote on his page of the Attack on Titan Fandom references closing himself off from the world: “I wished I could’ve stayed cooped up in my room, ears shut … But if I had, the burnt ashes of the dead would never have forgiven me.”

Source: https://www.distractify.com/p/why-does-jean-cover-his-ears