Multi-variable calculus is the application of the concepts of calculus to functions with more than one variable. For example rather than finding the area under a line when taking an integral one instead finds the volume (if the equation is a function of 3 variables).
As multivariable calculus usually involves a 3rd variable one will often find themselves working in 3-Dimensional Space.
Multi-variable calculus still uses the basics from both differentiation and integration but builds on one's methods and tool set to allow for working with multiple variables.
The two main concepts of multivariable calculus are the partial derivative and multiple integral which allow for calculus to be used on functions of multiple variables.
See partial derivatives.
See multiple integrals.