How did Europeans benefit from slavery?

For centuries (if not millennia), Europeans regularly relied on slave labor. Before the formation of Modern Europe, a significant portion of Ancient Greco-Roman society was comprised of people forced into different kinds of slavery ranging from total bondage to indentured servitude. In Ancient Athens, slaves made up as much as 30% of society. These slaves were mostly from nearby and surrounding areas, though war captives might be taken for slaves from farther away. With the collapse of the Roman empire, slavery in Europe really fell out of fashion and was replaced with serfdom. In the Byzantine empire, slavery persisted as a source of labor and slaves could be used as a sort of currency. Slaves might come from as far away as Ireland, having been captured by Norse raiders and traded across Europe. It was not until the 16th century that Europeans would once again rely heavily on slave labor and slave-produced goods.

On Columbus's voyages to the New World, he claimed both land and people for Spain. The colonizing of the Americas was not simply incorporating new territory on a map, but claiming anything and anyone found there as being for the benefit of the ruling nation. Along with tobacco and gold, indigenous Americans were brought to Europe as exotic relics from the New World. The enslavement of Indigenous Americans was less of a priority than the acquisition of goods and consumables from the New World, so, rather than import people into Europe, Europeans began exporting vagrants and criminals as laborers. As demand for labor increased in the Americas and New World diseases affected Europeans, the capture, sale, and enslavement of Africans became the preferred method of acquiring laborers.

By the 19th century, Europe had come to love and rely on a number of slave-produced goods, including coffee, tea, sugar, spices, precious metals and gems, tobacco, chocolate, and textiles. Slave labor is essentially labor that is free for the consumer, so the cost of a finished or consumable good was far lower than it would have been if laborers were compensated for their work. Some Europeans kept slaves in their homes as domestic servants, but this was really only done by the upper classes of European society. On the whole, European society benefited from slavery because it meant the goods they wanted could be created by someone other than themselves at almost no cost. 

Today, Europe is far less reliant on slave-produced goods and many nations continue to make efforts to ensure all working people receive a fair wage. Still, many of the garments sold throughout Europe are produced in nations where slave labor is still practiced.