Answer by taking a quote from the following article:

The indigenous peoples of the Americas are the pre-Columbian peoples of the Americas and their descendants. Although some indigenous peoples of the Americas were traditionally hunter-gatherers--and many, especially in the Amazon basin, still are--many groups practiced aquaculture and agriculture. The impact of their agricultural endowment to the world is a testament to their time and work in reshaping and cultivating the flora indigenous to the Americas. Although some societies depended heavily on agriculture, others practiced a mix of farming, hunting and gathering.

Indigenas or pueblos indigenas ("indigenous peoples") is a common term in Spanish-speaking countries, and pueblos nativos or nativos (lit. "native peoples") may also be heard, while aborigen (aborigine) is used in Argentina, and pueblos aborigenes (aboriginal peoples) is common in Chile. The term "Amerindian" (short for "'Indians of the Americas") is used in Quebec, the Guianas, and the English-speaking Caribbean. In Brazil, indigenas or povos indigenas are common if formal-sounding designations, while indio is still the more often-heard term (the noun for the Indian nationality being indiano), and aborigene and nativo being rarely used in Amerindian-specific contexts (e.g. aborigene is usually understood as the ethnonym for Indigenous Australians). Indigenous peoples are commonly known in Canada as Aboriginal peoples, which includes not only First Nations and Arctic Inuit, but also the minority population of First Nations-European mixed-race Metis people who identify culturally and ethnically with indigenous peoplehood. This is contrasted, for instance, to the American Indian-European mixed-race mestizos of Hispanic America (caboclos in Brazil) who, with their larger population (in most Latin American countries constituting either outright majorities, pluralities, or at the least large minorities), identify largely as a new ethnic group distinct from both Europeans and Indigenous Americans, but still considering themselves a subset of the European-derived Hispanic or Brazilian peoplehood in culture and ethnicity (cf. ladinos).  Indigenous peoples of the United States are commonly known as Native Americans or American Indians, and Alaska Natives.  Application of the term "Indian" originated with Christopher Columbus, who, in his search for India, thought that he had arrived in the East Indies. Eventually, those islands came to be known as the "West Indies", a name still used. This led to the blanket term "Indies" and "Indians" (Spanish indios, Portuguese indios) for the indigenous inhabitants, which implied some kind of racial or cultural unity among the indigenous peoples of the Americas. This unifying concept, codified in law, religion, and politics, was not originally accepted by the myriad groups of indigenous peoples themselves, but has since been embraced by many over the last two centuries. Even though the term "Indian" generally does not include the culturally and linguistically distinct indigenous peoples of the Arctic regions of the Americas--such as the Aleuts, Inuit, or Yupik peoples, who entered the continent as a second more recent wave of migration several thousand years before, and have much more recent genetic and cultural commonalities with the aboriginal peoples of the Asiatic Arctic Russian Far East--these groups are nonetheless considered "indigenous peoples of the Americas". The Portuguese and Spanish equivalents to Indian, nevertheless, could be used to mean any hunter-gatherer or full-blooded Indigenous person, particularly to continents other than Europe or Africa--for example, indios filipinos.

Why did he use the term Indian?
Columbus, who, in his search for India, thought that he had arrived in the East Indies.