Calculus-based heuristics, like Newton's method or gradient descent, use principles of calculus to find solutions to complex problems. They involve calculating slopes or gradients to understand how a function changes. For instance, gradient descent moves towards the lowest point of a function, similar to finding the bottom of a valley - this point is often the best solution. These methods are powerful for optimizing problems, like in machine learning or economics, where finding the most efficient point is crucial.