Slavery was a large and integral part of the world economy for centuries. During the 18th century, the largest slave trade in the world was the Trans-Atlantic Triangle Trade.
It was called the Triangle Trade because instead of going back and forth between two places as most trade does, it cycled through three, and made profitable trades at each point of the triangle.
Beginning in Europe, especially Great Britain, traders would first travel to Africa, bringing manufactured goods such as firearms and alcohol and trading them for slaves. It's a common misconception that the Europeans conquered and directly took slaves by force; this did happen a few times, but it was not the usual method. Instead, African slavers would capture people from enemy tribes, enslave them, and then the Europeans would purchase the slaves from those slavers. African slavery had been going on for centuries before Europeans ever got involved. Of course, the high demand for slaves from Europeans, along with the guns they provided for sale, surely made slavery in Africa much worse than it would have been on its own.
The next step in the triangle was to travel to colonies in North America and the Caribbean, where the slaves would be sold to plantations in exchange for goods, mostly agricultural products, that were difficult or impossible to obtain in Europe, such as tobacco, potatoes, and cotton.
Then, to complete the triangle, the traders returned to Europe and sold these "New World" goods for more manufactured European goods, pocketing the profits and beginning the cycle anew.
Without slavery, this triangle trade would not have been possible, and trade in general with the colonies in North America and the Caribbean would have dried up, unless European traders had found something else to sell the colonists. But most goods were actually quite abundant in the colonies, especially agricultural goods; mainly what they needed more of was labor. Firearms were relatively scarce, but European empires wanted it to stay that way, lest the colonies revolt (which of course many eventually did, notably the US).
The most viable mode of trade that wouldn't have been as horrifically evil as slavery would probably have been to bring free laborers, people who willingly came to North America to work and paid travel fees to do so. Of course, that wouldn't have been nearly as profitable for either the traders or the plantations, so in the absence of law or public outrage against slavery, the self-interested traders had little incentive to change.