The multiple integral is a generalization of the definite integral with one variable $\int f(x) dx$ to functions of more than one real variable, for example, $\iint f(x, y) \,dx\,dy$ for an indefinite double integral or $\iiint f(x, y, z)\, dx\,dy\,dz$ for an indefinite  triplet integral. For definite multiple integrals, each variable can have different limits of integration.
Thumbnail: Double integral as volume under a surface $$z = 10 − x^2 − y^2/8$$. The rectangular region at the bottom of the body is the domain of integration, while the surface is the graph of the two-variable function to be integrated. Image used with permission (Public Domain; Oleg Alexandrov)