Vocabulary - Prefix Sum

A prefix sum array stores cumulative sums. For array $arr$, the prefix sum $prefix[i]$ equals the sum of all elements from index $0$ to $i-1$.

$prefix[i] = arr[0] + arr[1] + \cdots + arr[i-1]$ We set $prefix[0] = 0$ by convention. So $prefix$ has length $n+1$ when $arr$ has length $n$. Why store cumulative sums?

Because any range sum you can compute from two prefix values. That's the core idea.