Keeping it brief and simple, $f(x) = y$ can be plotted in $xy$-plane. $f(x, y) = z$ can be plotted in 3D coordinate system. But what happens as we come across a function like this one $f(x, y, z) = w$. Can we plot it? In what system?
I have a picture of a book's page to explain my problem lucidly but it aint allowing me to put an image.
If you have a map $f:\>A\to B$ then the graph $${\cal G}(f):=\bigl\{(x,y)\in A\times B\bigm| y=f(x)\bigr\}$$ is a subset of the cartesian product $A\times B$. It follows that the graph ${\cal G}(f)$ of a function $f:\>{\mathbb R}^3\to{\mathbb R}$ is a subset of ${\mathbb R}^3\times{\mathbb R}={\mathbb R}^4$.
For ordinary humans it is impossible to visualize such a graph, which is a three-dimensional hypersurface in ${\mathbb R}^4$. But there are other means to obtain a "graphical" representation of such an $f$, e.g., the following: Imagine that $f(x,y,z)$ is the temperature in ${}^\circ$C at the point $(x,y,z)$. Then one could draw the isothermal surfaces of $f$. These surfaces foliate three-space as do the pages of a book, or the skins of an onion.
