Cleverness is the quality someone has when they're funny and smart or inventive. If you're wise and witty, your cleverness is likely to make school a breeze.
It takes cleverness to solve a tricky logic problem, and it takes a slightly different kind of cleverness to tell a joke really well or come up with a funny response. When a person is clever, they're either very smart and quick-thinking, or they're witty. The meaning of cleverness has evolved over time, including meaning "attractiveness" and "agreeableness" in some dialects.