What is the Gini coefficient?

The Gini coefficient is a measure of inequality. It is equal to 0 when there is no inequality (the economy's income is shared perfectly equally between all individuals) and up to 1 which is perfect inequality (1 individual holds all the income in an economy and everyone else has nothing.
This number is derived from the Lorenz Curve. The standard drawing of this curve looks banana shaped. Along the bottom we have the cumulative share of the population (from 0 - 100%) and then on the righthand-side we have the cumulative share of income in the economy (again, 0 - 100%). So on this diagram we can see how much income a certain percentage of the population owns, i.e. the bottom 50% owning 30% of income. A 45 degree line is also used, this represents equality so on this line the bottom 50% would own 50% of the income.
The Gini coefficient is defined as the difference between the perfect inequality line (A) and the Lorenz curve as a percentage of the total area below perfect inequality line (A+B) . So A/(A+B) this is the same as 2*A.
This is a really useful statistic as it is one simple number which allows us to make quick comparisons between countries or regions. But remember because it is just one number there is limited information we can derive from it. It is difficult to interpret what changes in the Gini coefficient represent, for example we wouldn't know whether a reduction in the Gini coefficient meant that the bottom 10% gained relative to the top 10% but it is a good overall indication.