I am trying to understand the following exercise from Introduction to algorithm (3rd edtion).
Exercise 24.1-3 (page 654)
Given a weighted, directed graph $G=(V, E)$ with no negative-weight cycles, let $m$ be the maximum over all vertices $v \in V$ of the minimum number of edges in a shortest path from source $s$ to $v$. (Here, the shortest path is by weight, not the number of edges.) Suggest a simple change to the Bellman-Ford algorithm that allows it to terminate in $m + 1$ passes, even if $m$ is not known in advances.
So what is $m$ exactly? I am really have the trouble to understand the first sentence.