Sometimes they use plots that show the number of new cases each day as a bar graph. That is easy to see what they mean by “flatten the curve”. The taller the bar, the more new cases. As the rate of new cases falls, the bars are shorter. The same is done with deaths.
The comparison charts being shown in the provided links are trying to compare numbers between locations that have different exposure start times, different population density, different responses on shut downs, etc. Every chart you see is manipulating, tweaking, and juggling the data to try to find some meaningful way to understand it. How bad is the disease, how fast is it spreading, which areas are being hit harder or faster, which are resounding better, etc.
If you are struggling to understand the charts, some of that may be your own disgraphia, understanding the nature of graphs, log scales versus linear, etc. But some of it is the choice in how to present the data - cumulative versus each day at a time.