The determinant of the matrix of its vectors gives the measure of an $n$-dimensional parallelogram.
For example, in $2$ dimensions, the area spanned by vectors $v$ and $w$ is \begin{array}{|cc|} v_1 & w_1 \\ v_2 & w_2 \\ \end{array} and so forth for a $3$ or more -dimensional parallelogram.
How is possible to visualize that, or understand that intuitively?