Intuitive understanding of determinant function definition(notation based on group theory)

Question

Here is the definition of the determinant function with n $v$ vectors. What I cannot undersant, what do exactly $\sigma(1)...\sigma(n)$ in this case mean?I know, that it means permutation of first element....permutation of n element. But how can I interpret this from intuitive point of view?

Answer 1

$\sigma(1)$ is the element that is at the first position in the permutation $\sigma$, and so one for $\sigma(2)$ etc..

E.g. if $\sigma(1,2,3)=(3,2,1)$ than $\sigma(1)=3$, $\sigma(2)=2$, $\sigma(3)=1$