Until the Age of Mechanization, Slavery, or something like it, existed with any large agrarian economy. The Northeast, in very early colonial times, began to diversify its economy, but labor through slavery was legal, so some slavery activity occurred. Slavery existed in the Northeast for the same reason it existed in the South, because it was tolerated, but not established to the same extent, as farming became less important to the Northeast economy over time. Just the opposite happened in the South, as agriculture was the sole economic activity and more lands westward continued to be settled and farmed. Had "Northern Virginia" (what the NE was known as in early colonial days) been as fertile as Virginia proper, slavery would have been as widespread in the North as in the South, and begs the question if the moral issue of slavery would have ever been raised. By accident of climate and geography, the Northern and Southern colonies were set on divergent economic paths from their first settlements.
Slavery has existed everywhere in the world at one time or another. The reasons are always the same, they are power, economy, and profit.
The slave trade in New York was begun by the Dutch who used slaves to work on their farms. Eventually the British began to get more involved in the slave trade. An interesting fact that I read in Enotes was that Africans were used because their skin color made them easy to identify if they ran away.
"The New York colonists used slaves in a variety of ways—on farms, in households, and in small factories. Slaves earned their keep in a variety of ways. Many slaves became skilled craftspeople, capable of doing any kind of work a city or rural area needed."
This is just one colony, remember that Europe had slaves before the Americas did, so when countries began to move into North America, they brought slaves with them. When the slave trade began to really take hold in the Americas New Hampshire was the largest trader of slaves. The colonies used them in fields, shipyards, on boats, and in factories.