Multivariable functions are mathematical functions that involve two or more independent variables. They are essential in various fields such as physics, engineering, and economics, as they help model complex systems where multiple factors interact. For example, a function that describes the temperature at different points in a room can depend on both the x and y coordinates of those points. These functions can be represented graphically in three-dimensional space, where the output value is depicted as height above a plane defined by the input variables. Understanding multivariable functions is crucial for studying concepts like partial derivatives and multiple integrals, which extend the principles of single-variable calculus to higher dimensions.