In graph theory, flow is defined on a capacitated network as an assignation of a flow number to each arc such that the flow of each arc is less than or equal to that arc's capacity, and such that the flow into each vertex (besides the source(s) and sink(s)) is equal to the flow out of that vertex. The second property is called conservation of flow. The total flow is defined as the flow out of the source (= the flow into the sink).
Basically, you've got a network of pipes with junctions between them, one junction where all the flowing stuff comes from, and another junction where all the stuff ends up. Each pipe has a limited capacity, and can only move stuff in one direction (one-way valves?). You can send your stuff through the pipes any way you like, so long as you don't overload any of them. One interesting problem is to find the maximum flow through a network.