Prof. Matthias Schonlau gave a presentation about "hammock plots" in New York recently.
Here is an example of a hammock plot that shows the progression of different rounds of voting during the 1903 papal conclave. (These are taken at the event and thus a little askew.)

The chart shows how Cardinal Sarto beat the early favorite Rampolla during later rounds of voting. The chart traces the movement of votes from one round to the next. The Vatican destroys voting records, and apparently, records were unexpectedly retained for this particular conclave.
The dataset has several features that brings out the strengths of such a plot.
There is a fixed number of votes, and a fixed number of candidates. At each stage, the votes are distributed across the subset of candidates. From stage to stage, the support levels for candidate shift. The chart brings out the evolution of the vote.
From the "marginals", i.e. the stacked columns shown at each time point, we learn the relative strengths of the candidates, as they evolve from vote to vote.
The links between the column blocks display the evolution of support from one vote to the next. We can see which candidate received more votes, as well as where the additional votes came from (or, to whom some voters have drifted).
The data are neatly arranged in successive stages, resulting in discrete time steps.
Because the total number of votes are fixed, the relative sizes of the marginals are nicely constrained.
The chart is made much more readable because of binning. Only the top three candidates are shown individually with all the others combined into a single category. This chart would have been quite a mess if it showed, say, 10 candidates.
How precisely we can show the intra-stage movement depends on how the data records were kept. If we have the votes for each person in each round, then it should be simple to execute the above! If we only have the marginals (the vote distribution by candidate) at each round, then we are forced to make some assumptions about which voters switched their votes. We'd likely have to rule out unlikely scenarios, such as that in which all of the previous voters for candidate X switched to someone other candidates while another set of voters switched their votes to candidate X.
***
Matthias also showed examples of hammock plots applied to different types of datasets.
The following chart displays data from course evaluations. Unlike the conclave example, the variables tied to questions on the survey are neither ordered nor sequential. Therefore, there is no natural sorting available for the vertical axes.

Time is a highly useful organizing element for this type of charts. Without such an organizing element, the designer manually customizes an order.
The vertical axes correspond to specific questions on the course evaluation. Students are aggregated into groups based on the "profile" of grades given for the whole set of questions. It's quite easy to see that opinions are most aligned on the "workload" question while most of the scores are skewed high.
Missing values are handled by plotting them as a new category at the bottom of each vertical axis.
This example is similar to the conclave example in that each survey response is categorical, one of five values (plus missing). Matthias also showed examples of hammock plots in which some or all of the variables are numeric data.
***
Some of you will see some resemblance of the hammock plot with various similar charts, such as the profile chart, the alluvial chart, the parallel coordinates chart, and Sankey diagrams. Matthias discussed all those as well.
Matthias has a book out called "Applied Statistical Learning" (link).
Also, there is a Python package for the hammock plot on github.