Revolution is definitely contagious. When one group successfully rises up and rids itself of the oppressor, it is natural for other groups to get the idea. This is similar with the French Revolution spreading to other colonies. There were many revolutions in a relatively close space of time.
At first the issue was the abolition of slavery, but it quickly became an issue of independence from France. In fact, the issues became conflated well after 1795, when troops sent by Napoleon occupied Haiti with the intention to reinstitute slavery. When L'Ouverture agreed to a compromise truce that would allow Haiti to remain in the French Empire, he was betrayed and imprisoned. It was not under L'Ouverture that Haiti achieved independence, but under Jean-Jacques Dessalines. And it took almost ten years of bloody struggle to achieve it.
When the French Revolution liberated slaves in the colonies, Saint Domingue, the former name of Haiti, was a long ways from Paris, France, and the French landowners on the island did not wish to liberate their slaves. So, the slaves entered into a revolt against their masters.
Three years later, in 1794, the French found themselves engaged again in war with England, and their troops were decimated. With this grave situation, the governor met with the chief of the slaves, Toussaint L'ouverture, and struck a bargain. L'ouverture told the governor his men would fight against the English if they could be guaranteed their liberty; the governor accepted. In July, 1795, Toussaint L'ouverture was Brigadier General and Vice-Governor of Saint-Dominique, leading the country to economic independence.
They rebelled largely because they didn't like being slaves. Of course, they'd been slaves for a while, so why did they rebel just right then? Mostly, that's because of the French Revolution. It made a big deal about liberty and equality and that made blacks in Haiti more hopeful that they would be able to get some of those things for themselves.