Something that's exhausting tires or fatigues you. An exhausting hike up the side of a mountain leaves you gasping for breath and so tired you need to sit down and rest.
Some things, like a rigorous workout or a difficult type of manual labor, are physically exhausting. Others are mentally exhausting, like a long argument with a friend or a tricky calculus exam. The adjective exhausting is rooted in the Latin exhaurire, "draw off, take away, use up, or empty," which perfectly describes how you feel after an exhausting experience.