The Devron 500 was a space race in the late 24th century, declared illegal in the Federation because it crossed the Romulan Neutral Zone. The races occurred at impulse speeds, with various hazards including uncharted black holes, rogue planets, dangerous nebulae, and Romulans.
When Sam Rutherford was attending Starfleet Academy, he had an illicit hobby of building racing ships in a private garage, which he funded with winnings from Devron 500 races.
In 2381, Rutherford's cybernetic implant malfunctioned and caused his pre- and post-implant personalities to struggle for control within his mind. The younger Rutherford proposed a race to determine the winner, to which the older agreed. He then manifested a randomized version of a Devron 500 race within their mindscape, with the younger Rutherford choosing to fly the Sampaguita and the older Rutherford the Delta Flyer. During the race, they came under fire by a D'deridex-class warbird; by manifesting his friends Beckett Mariner, Brad Boimler, and D'Vana Tendi for help, the older Rutherford evaded the attack and saved his younger self from the destruction of his ship, thereby winning the race. (LD: "Reflections")
The name of the race presumably refers to the Devron system.