The Lorenz curve is a graphical representation of the distribution or equality of something. The straight line from (0,0) to (100,100) shows perfect equality, whereas the line from (0,0) to (0,100) shows perfect inequality. The line drawn between these two lines is the actual measurement. The graph (shown above) shows the distribution of wealth through the whole country and it shows that the wealth is not equally distributed.
The Gini coefficient is a measure of inequality. It is the lightly shaded blue area of the curve and the higher the Gini coefficent the higher the inequality. The Gini coefficient gives a statistical number to measure inequality rather than a graphical display. The Gini cofficient is always measured between 0 and 1.