It explains many things never seen but clearly implied by the movies. Less a case of how it influenced future stories and far more the case of how it seamlessly interwove stories previously published into its story, giving the history behind things later in the chronology.
We have how Han learned to understand Wookiee as well as Hutteese. Where, how and why he learned to fly starships. How he was a respected officer in the Empire and went to a smuggler with a Wookiee with a life debt at his side. Of course, it also tells us how he won the Falcon. We even see him dump a shipment of spice that led to his trouble with Jabba. What got Han in so much trouble with Lando that he feared he might hold a grudge. We see his first brush with Rebels here and why he might have been so concerned about getting paid.
This story interweaves multiple characters and threads from the rest of the Expanded Universe. It also expertly weaves around Han Solo adventures by Brian Daley that occurred in the Corporate Sector, even giving why he went there in the first place.
Han’s Alias: Jenos Idanian, was later used by Corran Horn in I,Jedi
Togorians. The feline species later shows up in Knights of the Old Republic (comic) Knight Errant ,Jedi Apprentice, Republic (comic), Shatterpoint, Dark Times, Tatooine Ghost, Thrawn Duology, Survivor’s Quest, New Jedi Order, Dark Nest, Crucible.
Tlanda’ Til – Appear later in the New Jedi Order.
Ylesia – the planet is mentioned in various games and stories, and is visited in the New Jedi Order.
Bria Tharen – Han’s former girlfriend and fiance also appears in Underworld: the Yavin Vassilika by Dark Horse Comics.
Chewbacca’s marriage to Mallatobuck happens here. While she was introduced in the Wookiee storybook and the Holiday Special with their son, this is our first true look at events that lead into scenes from Chewbacca, the tribute comic by Dark Horse.
Salporin and Ralrracheen, (wookiees) from the Thrawn trilogy.
Mako Spince (smuggler), Shug Ninx (mechanic), Salla Zend (smuggler and lover) , Vima Da Boda (former Jedi / fortune teller) – Dark Empire
Kid DXo’ln, Zeen Afit, Wynni and Sinewy Ana Blue (smugglers) – The New Rebellion
Xaverri (stage magician and expert con artist out for revenge on Imperials) – The Crystal Star
Roa and Lwyll – (Smuggler who taught Han the Kessel Run and his wife) Han Solo Adventures (Han Solo’s Revenge)
Durga the Hutt (Rival of Jabba & Black Sun Vigo)- Darksaber and Shadows of the Empire
Thracken Sal Solo (Unwanted Relative) – The Corellian Trilogy
Senator Garm Bel Iblis, Winter (Leia’s aid and intelligence agent) – Thrawn Trilogy
Vuffi Raa (Droid) – Lando Calrissian Trilogy
Dash Rendar – Shadows of the Empire
Vima Da Boda (fallen/lost Jedi/ Vagrant) – Dark Empire