The optimality condition is necessary for distTo[u] to be the minimal length of paths from s to u.

If

      distTo[w] > distTo[v] + e.weight() for some v, w, and edge
      v-> w
   

The path from s to v followed by the edge from v to w would have total length

      distTo[v] + e.weight()
   

And so dist[w] would not be a minimal length for a path from s to w.