Let us assume that you have a finite length discrete signal $x$, denoted by its samples $x_n$, $0\le n<N$; $x$ does not depend on $n$, but its is values are indexed by $n$. Once you index a signal with integers, it somehow "looses" its dependence to an "actual time" in seconds. In other words, one does not know how much time actually elapsed between $x_{13}$ and $x_{14}$. And, in a relative way, one does not care, when it comes to understanding which (relative) frequencies compose $x$.
When we compute the DFT of $x$, we turn its $N$ values onto $K$ other values $F_k$ (most often $K=N$), indexed by $0\le k<K$. The $F_k$'s are Fourier amplitudes, relatively indexed by integers, but the Fourier transform, globally, does not depend on an integer.