I believe this would be called a stacked bar chart. It shows the proportion that each region makes up in a larger sample of Islamic regions and how this changes across time (broken up by 50-year periods).
It is difficult to interpret at first because it is in grayscale and the authors use a non-intuitive way of describing what is shown.
Iraq's substantial importance under the Abbasid caliphate, for example, is quite clear as is its rapid decline following the Mongol invasions of the 13th century and its virtual obliteration after the time of the Timur around A.D. 1400
You can see this pattern they are describing as Iraq makes up a large proportion on the y-axis from A.D. 695 ~ A.D. 1228, described as "..substantial importance under Abbasid caliphate", and then that proportion becoming smaller after this ("..rapid decline following Mongol invasions of the 13 century..") and continuing to shrink until the end of the x-axis (.."virtual obliteration after the time of the Timur at A.D. 1400").
Here is another example of a stacked bar chart - Stacked Bar Chart.