This is a bit of a long answer, so strap yourself in.

Cuba's economy up until the 1790s was essentially a mix of small plantations in and around ports, a smattering of tobacco cultivation in important areas (particularly the West, in today's Pinar del Río), subsistence agriculture, and cattle ranching. Havana itself also had an important service industry, satisfying the needs and wants of the Spanish fleets which used Cuba's foremost city as their last stop before returning to Europe. Enslaved Africans had been part of Cuban society since at least around the 1520s, when the first known slaving vessel landed in a Cuban port and sold its human merchandise, but the slave population was nowhere near a majority of the total population, slaves often achieved emancipation and were able to develop a strong community of free people of color (including the formation of creole militia batallions just for people of color), and the treatment of slaves was usually tempered by their value (it was unusual to work a slave to death since their value was so high relative to the value they produced).

This ended when the region's foremost plantation economy, Saint Domingue, collapsed in what became the Haitian Revolution. Local elites in Havana, who had been articulating economic projects since at least the early 18th century, found a voice in the "Discourse on Agriculture and Ways to Foment It" by the city's own Francisco Arango y Parreño around 1792. This was a project to turn Cuba, and more specifically Havana, into the next major plantation economy, taking advantage of the removal of their main competitor (Haiti) from markets and the soaring prices which resulted from increased demand and reduced production. As Manuel Moreno Fraginals points out in Cuba/España España Cuba, creole elites on the island weren't true colonized subjects until the Liberal constitution of 1837. From as early as the 16th and 17th centuries, local elites had intermarried with key government officials and wealthy families in Spain and by the late 18th and early 19th centuries they were able to work these connections into real changes in colonial policy which provided all the concessions they needed to jump-start a real plantation economy in the region. Taxes were reduced or temporarily waived for new plantations, neutral commerce was permitted and by the 1810s and 1820s codified into a limited open port system, bureaucratic red tape was reduced, and a free and ready flow of African slaves was encouraged. Everything a growing slave economy needed.

Some historians, like Cuban Marxist historian Jorge Ibarra, call this a Plantation Revolution in terms of the island's economy and colonial politics. This new colonial compact, of active collaboration between Spanish officials and local creole elites, combined with booming economic prosperity and the fear of political change portending social revolution (such as occurred in Haiti) helped keep Cuban creole elites firmly anti-separatist while the rest of Spanish America was torn apart by separatist uprisings.

For the first time in a long time, perhaps the island entire history, the colony was in the black. Previously, shipments of gold and silver from New Spain (a practice known as the situado) had been compensating for the high costs of garrisoning, fortifying, and generally administering the island's economy. But now, Cuba's prosperity was a key source for Spanish colonial income (especially after losing most of its American colonial empire).

Now, what did this mean for enslaved and free Africans in Cuba? Nothing good. From a semi-patriarchal relationship with masters who could ill afford to work their slaves to death, the Cuban slave plantation ballooned in the late 18th and early 19th centuries to giant affairs involving dozens of workers or more. Plantations exhausted the land, the need for firewood to stoke the flames of the sugar cane juice purging process devoured the forests (creating the savannah that still exists around Havana), and slaves were used up and replaced in the same way you would use up easily replaced and essentially interchangeable parts of farm equipment. Soaring sugar prices meant that as long as you could squeeze enough value out of slaves before they collapsed and died or became crippled, you could treat them poorly and work them to death.

Emancipation rates dropped as many slaves as possible were sent to feed the insatiable need for more laborers. Free people of color survived but they were increasingly seen as a caste, especially as the pseudo-scientific myths about race help legitimize old prejudices (one Spanish official around the 1830s caused a scandal by referring to black children as "niños" instead of "negritos", meaning little blacks, or "cachorros", pups).

During the first half of the 19th century, as things got progressively worse for free blacks, the black militias known as the Batallones de Pardos y Morenos became focal points for conspiracies inspired by numerous sources including the Haitian Revolution. Several officers in the militia were even linked to the infamous Aponte Rebellion (a slave uprising) in 1812. The lowest point for people of color came by the mid-century when people of color (between slaves and free folk) came to form a slim majority on the island. This left otherwise level headed reformists, like José Antonio Saco, warning in apocalyptic terms of the danger of "Africanization" that Cuba faced and warning that a rebellion against Spain would result in the destruction of the white race. This fear, it should be said, was quite capably fanned by the Spanish government to undermine separatist inclinations on the island.

When the so-called Conspiración de La Escalera (Ladder Conspiracy) was discovered in 1844, being more organized and more widespread than any before, the colonial government together with fearful white creoles instituted the equivalent of a Night of the Long Knives against free people of color. The conspiracy was seemingly blown out of proportion, whether by paranoia, opportunistic whites who wished to cull the black population like Spartans culled the helots, or a combination of both, the end result was clear. The colored militias were disbanded. Blacks considered too opinionated were arrested, killed, or exiled. Anyone who was thought to be a potential threat was dealt with in some way. One such case, renowned black Cuban poet Juan Francisco Manzano, was wrongfully arrested and detained, being treated in such a way that by the time he was freed around a year later he was a broken man.

In my mind many a parallel can be drawn between the change in the character of slavery in the US during the same period, with slavery increasingly becoming a social caste with the enslave finding it ever more difficult to be freed or even survive until emancipation.

As a final note, yes, the slave trade was outlawed in the 1820s thanks to British pressure on the Spanish monarchy (using its numerous loans to that particular Bourbon dynasty as leverage) but a black market slave trade continued with the connivance and collaboration of government officials knowing that Madrid had only bowed to London due to pressure and not genuine desire to end the trade (in addition, bribes kept officials happy). As the Brazilians said about their own black market slave trade after the British pushed their government to accept the abolition of the legal trade, it was a "law for the Englishman to see", but not to be enforced.

Books and sources:

For English only readers, I'd suggest the pertinent article in Leslie Bethell's Cambridge History of Latin America on colonial era Cuba as a good place to start. For more, see sources below.

Manuel Moreno Fraginals: El Ingenio and Cuba/España España/Cuba.

Matt Childs: The 1812 Aponte Rebellion in Cuba and the Struggle Against Atlantic Slavery

Jorge Ibarra: Varela el Precursor: Estudio de una Época

Jacobo de la Pezuela: Historia de la Isla de Cuba

Maria del Carmen Barcia: Poder étnico y subversión social: Los Batallones de Pardos y Morenos en Cuba (found this as a scanned PDF online: http://www.angelfire.com/planet/islas/Spanish/v1n1-pdf/06-09.pdf)