You have an Eddington number E if you have ridden E days covering at least E miles. So for example, if you had an Eddington number of 75 it would mean you have ridden at least 75 miles on 75 separate days *(sorry, you probably knew that already, but it helps with the explanation below)*.

The charts show the number of days (vertically) in which each of the riders have ridden at least a given distance (indicated by horizontal position). Using Steve an example, the line starts off high on the left hand side because he has had around 300 days when he has at least ridden 1 mile. It remains quite high towards the left because he has also had around 300 days when he has ridden at least 25 miles. The line starts to drop as the distance ridden in a day before it is counted increases. So for example, there have only been around 10 days when he has ridden at least 250 miles.

The diagonal grey line represents the 'Eddington line' because it joins all the points where the minimum distance ridden matches the number of days that has occurred (all the Es). That allows you to see a rider's Eddington number as it is where their own line intersects that diagonal.

The point made by SimonP above was about the shape of the curve made by each rider as you can imagine different archetypical riding styles. A super-consistent rider who rode 200 miles every day would have a rectangular shape where from left to right they would have at 200 days of at least 1, 2, 3,...200 mile rides and then 0 days of 201 miles or more. Kurt is showing something approaching this kind of profile. In contrast a rider who had a lot of variation in the length of rides they do would have a curve that gradually fell as it moved right (they'd have many days of at least 1 mile, a few less of at least 10 miles, fewer still of at least 50 miles etc). Miles shows this kind of profile.