EU Allusions
First off, it’s worth pointing out that, while Solo creates its own origins story for Han, it does draw a fair amount from the Expanded Universe – despite what writer Lawrence Kasdan recently said.
In the old expanded canon, Han’s homeworld of Corellia was known for producing the best pilots and spaceships. In the movie, the planet is nowhere near as nice a place to live, as it’s depicted as an industrial, crime-ridden hellhole, but it’s still a hub for spaceship construction, albeit under the orders of the Empire.
Han is likewise revealed to have been an Imperial pilot for a time until he deserted his post. In the novels, he flees when he frees Chewbacca and some other Wookie slaves, while in the film it’s fairly similar, as he runs away after he hatches a plan to escape with his future fuzzball friend. The EU marks this as establishing Chewie owing a life debt to Han, which is why he never leaves his side from then on. The movie doesn’t make any mention of this, though.
Han’s Gold Dice
Han’s lucky golden dice – or chance cubes, if you want to use the official in-universe name for them – used to be a minor background detail that could be glimpsed hanging in the Millennium Falcon’s cockpit from A New Hope onwards. However, they gained a lot of extra significance in The Last Jedi, when they were used to symbolize Han’s passing in the emotional finale to that movie.
In Solo, their prominence continues, as they reappear throughout. Though we don’t get to find out exactly where Han got them, we do learn that they’ve been his lucky charms through his tough life on the streets. He gives them to Qi’ra for luck, and doesn’t get them back until they reunite years later.
At the end of the movie, he hangs them up in the Millennium Falcon, where they’ll stay until Luke finds them after his death. You can theorize that, to Han, they represent the struggles of his youth, but also act as a memory of his relationship with Qi’ra.