Partial derivatives are a way to understand how a function changes when you change just one of its variables, while keeping the others constant. For example, if you have a function that depends on two variables, like x and y, the partial derivative with respect to x shows how the function behaves when only x changes, ignoring any changes in y. In practical terms, partial derivatives are essential in fields like physics, engineering, and economics, where many factors influence outcomes. They help in optimizing functions, such as finding the best design for a bridge or maximizing profit in a business scenario, by analyzing the impact of individual variables.