The horizontal axis shows income level per person. You should think of this axis as broken down into small segments that are each $20 in width. Then, vertical axis shows what share of world population receives that income level, for each $20 segment of income. (If you used income widths greater than $20, the overall shape of the green, red, and blue lines would be essentially the same, but because the width of the "bins" would be larger, the numbers on the vertical axis would be larger, too.)
The green line shows distribution of global income in 2003, the red line in 2013, and the blue line is a projection for 2035. You can see the median and mean income distributions rising over time. The overall flattening of the income distribution over time as a smaller share of the population is bunched at the bottom tells you that the income distribution is getting more equal. On the graph, inequality is measured by a "Gini coefficient," which is a standard measure of inequality.
For quick intuition, I'll just say that the Gini coefficient is measured along a scale from 0-100, where zero means complete equality of incomes, and 100 means that a single person receives all the income. To get a more intuitive feel for what the Gini means, the World Bank publishes estimates of Gini coefficients, when data is available, for countries around the world. Countries with a very high level of inequality, like Brazil, Mexico, Zambia and Uganda, have a Gini around 50. In the United States and China, the Gini is about 40. In Germany and France, it's about 30. In highly egalitarian countries like Sweden or Norway, it's closer to 25. It's not especially surprising that the global Gini coefficient is higher than the Gini for any given country: after all, global inequality is greater than inequality within any given country.
If you would like a more detailed explanation of how a Gini coefficient is calculated, you can check out my earlier post on "What's a Gini Coefficient?" (April 3, 2014). One of the bits of intuition given there goes like this: "A Gini coefficient of G per cent means that, if we take any 2 households from the population at random, the expected difference is 2G per cent of the mean. So that a rise in the Gini coefficient from 30 to 40 per cent implies that the expected difference has gone up from 60 to 80 per cent of the mean."
Thus, in the figure above, in 2013, the Gini coefficient is 64.9 and the mean income is $5,375. Thus, if you pick at random two households from anywhere in the world, the average difference in their incomes will be 2 x (.649) x $5,375=$6,976.
