The cartoon in the link you have provided shows that the French Revolution was caused by anger among the Third Estate over their place in French society. The cartoon shows the Third Estate carrying the other two estates on its back. This symbolizes how the other two estates essentially lived off the work of the Third Estate and did not allow the Third Estate to have much in the way of rights.
Before the revolution, there were three estates. The First Estate was the clergy. It numbered about 110,000 people in France. The Second Estate was the nobility. There were about 130,000 people in this estate. Finally, there were the commoners. They were the Third Estate, numbering about 25 million people.
The Third Estate consisted of rich and poor people alike. A person could get rich from working hard as a merchant (for example) but could never move out of the Third Estate. The Third Estate, even though they were very numerous, had only one vote in the Estates-General, just like each of the other estates. The Third Estate was taxed much more heavily than the other estates (this is why they are carrying the other two) but yet had very little in the way of rights.
For these reasons, the Third Estate was very unhappy with the state of affairs, helping to cause the Revolution.
The French Revolution was principally caused by the growth in dissatisfaction among the poor and middle class of French society towards the nobility and the clergy, comprising, respectively, the Second and First Estates. French society was heavily structured to provide the maximum political power to the two percent of the population represented by the First and Second Estates. The cartoon, which depicts representatives of the First and Second Estates being carried on the back of the representative of the Third Estate, symbolizes the exploitation of the poor and middle class by the elite. In fact, the hunched over representative of the Third Estate is depicted leaning on a pick-axe, further symbolizing his peasant origins and status, a particularly significant point given that this estate included, as noted, the middle class as well as the poor.
To fully understand the causes of the French Revolution, and the significance of the political cartoon, it is important to keep in mind the precariousness of the First and Second Estate's positions despite their wealth and power. Any time two percent of a population controls the other 98 percent--and, in addition, the fact that the Third Estate paid virtually 100 percent of the taxes, with the Second Estate paying no taxes at all further served to inflame passions against the ruling elite--the odds of the two percent's survival are precarious indeed. Even the structure and practices of the nation's Parliament, comprised of a majority of representatives from the Third Estate, were heavily tilted against that majority. Toss into the mix the continued profligacy of the monarchy, despite the financial strains it was under courtesy of its support for the American Revolution, particularly the financial recklessness of Queen Marie Antoinette, and France was ripe for revolution.
The political cartoon, in conclusion, illuminates the burden endured by the Third Estate to the benefit of the two percent of the population comprising the First and Second Estates. That pick-axe the guy is leaning on is not just a tool, but, in the hands of a really angry peasant, a potential weapon of some lethality.