After Columbus "discovered" the Americas, the European empires each wanted the land to expand for more power. They expanded and conquered the indigenous populations, but there was one thing they lacked: Manpower. The indigenous populations were often too sick to work for the Europeans, and the Europeans weren't used to the hotter climate of South and Central America.

However, there were slave traders in Africa to provide labor for the American colonies. Slaves had been traded for centuries in Africa, and slaves had been traded to Europeans in the past through North Africa. Typically, slaves were traded for European goods, and most were brought to South America.

Since you asked about the US, I'll focus on the British side of things. First, the British didn't called the slaves "slaves." They were often classified as indentured servants and apprentices for life, like a worker coming from England. In the 1700's, slaves became more oppressed and slaves were now a racial caste. An ideology of racism, that still sticks around today, was formed treating the Africans as beasts to be bought and sold. It was abolitionism that ended the arrival of any new slaves in the United States in 1809, and in 1853, the Slave Trade was outlawed entirely. After the Civil War ended slavery and the African American Civil Rights Movement struck down racist laws, the oppression was mostly over, although racism still persists in the USA.

So, to answer your question, it was always there because they were an underclass to begin with back then, but became worse as time went on, then became better as abolitionism started to spread.

African slaves answered a need for labour in the New World as an initially small European population set out to colonise and exploit its new subject lands. Slavery wasn't unique to the North American Colonies, or to the Americas: slaves had been imported in smaller numbers into Atlantic Europe and nearby island territories from the mid-15th century, and European shipments of African slaves to Spanish America and Brazil started in the 16th century in response to a labour shortage occasioned by the decimation of native populations through unfamiliar disease. Facing a similar shortage, the northern Colonies began importing slaves from about 1630, though their precise legal status as "property" devoid of any rights only developed gradually around mid-century.

Africans were brought to Britain, but a number of legal judgements ruled that they remained persons before the law, unlike those shipped across the ocean (there were also rulings to the contrary in the 17th century, but the 18th saw a movement toward freedom on British soil).

It was generally better to be black in Britain, though Britain of course bears much of the responsibility for the sufferings of those transported to the Americas.