Note: Before reading this node, it is highly recommendable to have some notion of calculus. Please be familiar with calculus or the contents of that node before reading further.

Simply put, multivariable calculus is the study of calculus with more than one independent variable. Vector calculus depends heavily on multivariable calculus. Often times, when this subject is taught, only the two-variable case is dealt with, and "these results extend to as many variables as you may be working with" is a common mantra.

Some highlights:

The notion of 'derivative' is replaced with 'directional derivative'.
Some area and length calculation questions become easier. See Green's Theorem for specific function alterations.
Fluid mechanics becomes available as an area of study. Concepts like irrotational, divergence and gradient become important.

Since I took my time about updating this w/u, another, admittedly better, one has appeared. I think my generalizations and the other's specifics are a good combination, so I won't try to re-do all the work already done.