That’s a rather broad question, so I’ll try to stick to a broader answer without getting too far into the details. I’m happy to elaborate on specifics if you’d like.

As far as organization goes, the Haitians had clear leaders from the very onset of the revolution. An effective leader and a voodoo priest, Dutty Boukman organized the uprising in 1791, and inspired fanatical loyalty in those who served under him. In his footsteps, Jan Francious, Jeannot Bullet, and Georges Biassou took up the reins of the revolt and secured passive Spanish assistance from across the Santo Domingo border. Toussaint Louverture would eventually arrive on the scene as well, and would inspire the same sort of loyalty as his predecessors, while also boasting a deft military and political skillset. There were of course factions, but Toussant would eventually consolidate all of the slave revolutionaries under his control. He would persistently battle the enemies of the revolution, which were terribly divided. More on that later.

The Haitians also had a clear numerical advantage. On the eve of the revolution, 90% of Saint Domingue’s population was enslaved. That’s 500,000 people about to violently turn on their oppressors. Of the 30,000 whites on the island, only a few thousand were actually under arms. For the first several years of the revolution, all the whites could do was retreat to a handful of cities while the former slaves took control of most of the island.

The tenacity of the Haitian fighters played a significant role as well. Because of the abhorrent conditions slaves suffered under in Saint Domingue, the slave population couldn’t even sustain itself, and new slaves were constantly being brought in by the thousands. They brought with them their experience with African tribal warfare. Ambushes, feints, false retreats, and fearless aggression characterized the slave fighting force. Their beliefs in the power of Voodoo further bolstered their resolve. Many were convinced that certain objects would grant them protection, or essentially make them bullet-proof, leading to fearless charges into European formations. Needless to say, the outnumbered European forces were not terribly successful militarily. Even if they did succeed in taking ground, the slaves would often melt away into the countryside and simply reoccupy the position once the French moved on.

Back in Europe, France would find itself at war with most of Europe’s major powers come 1793, and the only assistance they would send to Saint Domingue were several groups of commissioners to attempt to remedy the situation. Naturally, the commissioners weren’t going to convince 500,000 former slaves to peacefully return to bondage. France’s opinion on the status of the slaves, especially in the context of the liberal ideals that began to dominate the political landscape in Paris, was also ever-shifting. Both pro-slavery plantation owners and anti-slavery activists lobbied the government in Paris. As for those in Saint Domingue who opposed the slave revolt, disunity was the name of the game. There was a constant power struggle between free people of color, poor whites (petit blancs), wealthy whites (grand blancs), the commissioners from the metropole, and the colonial authorities. All of these factions were fighting each other as well as the former slaves (except when they used slaves as soldiers to fight another faction’s slaves in slave-on-slave proxy-wars), and all were doing everything they could to ensure that when the dust settled, their faction would come out on top in the new order. That’s not to mention the opportunistic British forces that entered the fray seeking to undermine French efforts to reassert control of their colony. So, not exactly a recipe for ending a slave revolt half a million strong. Meanwhile, you have the very competent Toussaint leading a massive slave army with single-minded effectiveness.

Disease was always a major ally to the revolutionaries. The first thing European soldiers tended to do after landing on Haiti was to promptly drop dead of some terrible tropical disease. This is a problem that plagued everyone, from the initial French reinforcements from the Metropole to the British opportunists to Napoleon's expeditionary force that landed in 1802. The initial wave of death often exceeded 1/3 of any given expedition of European troops. An expedition of 7,000 British troops in 1794 saw 5,000 dead from yellow fever alone. Napoleon’s expedition to reinstitute slavery in Saint Domingue met similar results – no more that 8,000 of the 31,000 sent to retake the island returned. The overwhelming majority died of disease, rather than combat. With most of the European soldiers either sick or dead from terrible diseases, they struggled to assert dominance over the squabbling factions, let alone over the former slaves.

So, the Haitians had a lot of things going for them, and the French had a great deal working against them. Most of this can be found in any history of the revolution. David Geggus, Jeremy Popkin, Laurent Dubois and John Garrigus have all written comprehensive histories of the Haitian Revolution, and they’re the ones I am most familiar with. I’m familiar with a number of more focused publications as well if you’d like recommendations on something more specific.