The being known as Q was the son of Q and Q. He was conceived in order to end the hostilites of the Q Civil War, and was midwifed by Doctor Selar.
Q was the only child of two Q ever produced (with the exception of Amanda Rogers) and, as such, would come to possess power that singlehandedly rivaled that of the entire Continuum. The Continuum permitted such an act out of concern for some approaching threat, eventually discovered to be the encroachment of Omega into the multi-verse.
In 2381, Q discovered that the death of his god-mother, Kathryn Janeway was what the Q referred to as a "fixed point in time." Her death was an event which the multi-verse insisted occur across all universes in which she existed. Q investigated this unique phenomenon and also discovered the baffling fact that there existed a point in the future to which he could not travel -- an impossibility for the Q. Eventually, believing that Kathryn Janeway was the only individual capable of solving the approaching threat (as she once had in an alternate timeline within which it took Voyager 23 years to reach home), he broke the rules of the Continuum against resurrecting the dead by teaching Janeway's spirit how to bring herself back to life with the aid of Kes. The threat to his existence was eventually discovered to be the encroachment of the Omega Continuum into the multi-verse and the threat by Afsarah Eden to wipe the Q species out of existence. After receiving help from Icheb and giving Miral Paris the gift of never again being her people's messiah (as the Q had expected him to be for them), he and Afsarah Eden (his counterpart for the Omega Continuum) sacrificed themselves to seal the rupture between the multi-verse and the Omega Continuum into the multi-verse without having to destroy the Q. In the end, Q's mother forgave Kathryn for her involvement in her son's decision to sacrifice himself, but Q's father, Q, swore that Janeway had made him her enemy that day.