Double integrals are a fundamental concept in calculus that allow us to compute the volume under a surface defined by a function of two variables. They extend the idea of single integrals to higher dimensions, enabling the calculation of areas and volumes in two-dimensional regions. By integrating a function over a specified area, we can find quantities such as mass, charge, or probability. To evaluate a double integral, we typically set up the integral in iterated form, integrating first with respect to one variable and then the other. This process can be visualized as summing up infinitesimally small volumes over a region in the xy-plane, providing a powerful tool for solving complex problems in physics and engineering.