I'm reading Jungnickel's Graphs, Networks and Algorithms. He defines the flow as a mapping $f:E\to \mathbb{R}_0^+$, which seems to mean the value of the flow of each edge, but in here:
When he says "a flow $f$ is said to be maximal if $w(f)\geq w(f')$" he seems to be talking about all the edges, mainly because he uses the idea of value which is the flow of some of the edges of the network.
In the first case, he seems to be talking about a value that every edge has, in the second case, he seems to be talking about more than one edge. So, does flow actually mean two things?
A flow $f$ has a value $w(f)$. If $f$ is maximal, then no other flow has a value larger than $w(f)$. That's all the definition is saying.
Note: The flow value is the total amount of fluid being pushed from the source to the sink. It is affected by the capacities of each edge, but it is not the value of an arbitrary edge.