Quinn was a Q, and a member of the Q Continuum. After convincing the Q to take his powers from him and make him into a mortal being, this particular Q took the name Quinn.
Quinn served as one of Q's mentors in the distant past. Like the other members of the continuum, Quinn spent a great deal of time exploring the universe, and had spent several hundred years visiting Earth. During his visits to Earth, Quinn had influenced human history and directly touched the lives of several people.
During the mid 17th century, Quinn was in England when he sat down next to an apple tree, with Sir Isaac Newton seated opposite him. Quinn got up to leave, and jostled the tree, causing an apple to fall from the tree, striking Newton in the head, and gave Newton the inspiration to begin a new era in human science. If it had not been for Quinn, Q remarked that Newton most likely would've died in a debtors' prison, and would be a suspect in the murder of several prostitutes.
Later, in the 19th century, Quinn had taken the guise of a Union Army solider during the American Civil War, and was present at the Battle of Pine Mountain, Georgia. Quinn saved the life of a Union Army Colonel named Thaddius Riker - who was a distant ancestor of Kyle Riker and his sons William and Thomas. Without Quinn's help in getting him to safety, Thaddius most likely would've died at Pine Mountain, and not had any children. While Q sarcastically remarked that he would've missed several opportunities to insult William Riker over the years, the absence of Riker may have had far more profound consequences for humanity.
When Thaddius Riker believed himself to be dying, he asked Quinn to deliver a message to his family. In 2371, he delivered the message to William T. Riker that he should pursue his relationship with Deanna and to seek out his own command as to not make the same mistakes that Thaddius made. When Quinn encountered Riker on board the USS Voyager several years later he didn't allow Riker to have any recollection of their previous meeting.
Quinn was still on Earth in the 20th century when he offered a ride to a man named Maury Ginsberg to the Woodstock Music Festival of 1969. It was Ginsberg who noticed that a disconnected cable that had the potential to ruin the concert. Quinn also met his future wife, who had been sitting in Quinn's jeep. Thanks to Quinn's influence, Ginsburg became a successful orthodontist who had four children with his wife.
Aftrwards, Quinn became bored with his life, feeling that as an immortal being that he had lived so long that he had seen and done everything possible. Quinn attempted to commit suicide several times, once causing the Romulans and Vulcans to engage in a 100 year war as a result. The Q Continuum responded by imprisoning Quinn in a comet for the next several hundred years.
In 2372, the USS Voyager encountered the comet, and accidentally freed Quinn from his prison. The Q Continuum sent Q to place Quinn back in his prison, and Quinn asked Captain Kathryn Janeway for asylum on Voyager. Tuvok once asked him with such physical and mental advancement as the Q, did manners along the way de-evolve with them. In the following hearing, Quinn was able to convince Janeway and Q to grant him asylum, and Q stripped him of his powers. Quinn became a crewman on Voyager, but later committed suicide when provided with some Nogatch hemlock by Q.
Quinn's actions later led to a brief civil war in the Q Continuum, which was finally resolved when the first Q child in many thousands of years was born.