Simon Rowe explains what a Sankey diagram is:
In the image, you can see how Sankey used arrows to show the flow of energy with the widths of the shaded areas proportional to the amount of heat loss as it progresses through the engine’s cycle. This series of complex relationships would be difficult for a reader to understand at a glance were they simply presented in text and data tables. Making just such a sophisticated system easier to understand is the purpose of a Sankey diagram, which visually summarises the volume and direction of flows through the stages of a process or system.
Click through for several good examples, some advice on when a Sankey diagram could make sense, and the times in which you should not use this visual.