In American universities, EALC refers to East Asian Languages and Civilizations (or Cultures), and is the term for the department of East Asian studies, which studies this region of the world.
In terms of scope, the region is East Asia, however defined – roughly, the Sinosphere (region of traditional Chinese cultural influence), and can be narrowly defined as China and Northeast Asia (China, Japan, and Korea), as at the University of Chicago, or more broadly to also include Vietnam, Mongolia, and smaller groups such as Manchuria and Uyghurs – hence shading into Southeast Asian studies and Central Asian studies – as at Harvard.
The department name, which features "Languages", is because of the central place that language learning plays in these studies – primary research and most secondary research in the region requires faculty in the language, but due to the foreignness of East Asian languages (compared with English), students frequently require 4 or 5 years of coursework in the language before they have sufficient faculty to pursue studies. In the Sinosphere specifically, the time required to learn Chinese characters further adds to the time required, and thus EALC is a rather demanding course of study for those who do not already speak one of the languages in question.
By the graduate level (and advanced undergraduate), students are expected to have faculty with the language, and are frequently involved in then teaching it.