The term is thought to originate in the Nova Age as an insulting epithet to be used against novas. The name was also adopted by an activist group of novas who were fighting the perceived depredations of Project Utopia and the secretive Project Proteus.
Later, the Aberrants joined with another group of novas called the Teragen in the inevitable lead-up to a massive conflict. As the Teragen Chrysalis process removed a nova's connection to humanity, and the use/abuse of a nova's powers lead to progressively greater mutations, the nova populace became increasingly hostile to the remainder of humanity. At some point before the start of the Aberrant War, the term "Aberrant" grew to encompass all novas.
Thanks to the powers of Aberrants such as the Colony, not all "Aberrants" are truly Aberrants; rather, they are often "sub-Aberrants," otherwise normal humans who have been injected with Taint, resulting in mutations and a slavish devotion to their true Aberrant master.