A Sankey diagram is "a specific type of flow diagram, in which the width of the arrows is shown proportionally to the flow quantity." The Wikipedia link talks about energy flow, but style of the graph is used for other things. More helpful than a general definition is an example, like the Sankey diagram above made by flashman, named How 52 ninth-graders spell 'camouflage.' You can see exactly how many students diverged in their spelling as the word gets longer.
This may look like it would be complicated to graph, but there is a Sankey diagram generator called the Sankeymatic that will do it for you. You enter the data, and the graph comes alive. See examples of how people are using it at the Sankeymatic Twitter feed.