Separable and non-separable function

Can someone explain to me what is the difference between separable and non-separable function? I found some explanations, but these explanations are not in "human form". For example, I found that separable function can be expressed like this:

g(x,y) = gx(x)gy(y).

It is fine, but can someone explains it in "human form"? I mean some easy sentence, which describes what is a separable function, without some mathematics notation.

Thank you very much.

My suggestion for a "human form" explanation is that if you were plot a separable function f(x,y) you could just look down the x-axis and see a "one-dimensional" function g(x) (technically g(x) = f(x,0)). Any other one-dimensional function parallel to this one (parallel to the x-axis) would be a vertically-scaled version of this function.

It is the "continuous" version of a matrix formed by an outer product, so perhaps the following example gives the full gist of it. We "should" be calling matrices like this one "separable" matrices:

$$\begin{bmatrix} 1 & 2 & 4 & 7 & 2\\ 2 & 4 & 8 & 14 & 4\\ 5 & 10 & 20 & 35 & 10 \end{bmatrix}$$

Note that each column is a multiple of any other column, and the same is true of the rows. The graph of a separable function would have the same property.

It should be clear now that knowing just one row and one column is enough to defined the whole matrix. This fact answers the last question: yes, it is true that a separable function (in N-variables) can be defined using just N 1-variable functions.