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Afrocentrism is an approach to world history that focuses people of African descent, typically black Africans. With regards to Egyptology it is normally associated with a set of claims that the people of ancient Egypt were primarily or originally black Africans; adherents to this idea tend to rely on older sources, but do not always interpret them in the correct context - specifically, ideas of race and skin color current in today's society are not the same as they were thousands of years ago.
Afrocentrism in Egyptology is a direction reaction against the "ancient Egyptian race question" - a trend in late 19th/early 20th century anthropology to question whether or not the ancient Egyptians were white according to contemporary racialist standards. This has addressed in previous questions like How would an Egyptian in Alexandria at the end of the 1st Millennium BCE have perceived race and skin tone? by /u/cleopatra_philopater and Monday Methods: "No but what race were the ancient Egyptians really?": Race as a concept in history by /u/commiespaceinvader