Jango Fett's son Boba was a clone of himself. But he had another son, too.
Throughout his life, Jango visited countless worlds, which is only natural given that he was a bounty hunter. Consequently, he developed the idea that he would never truly have a chance to find true love, start a family, any of that. Subsequently, he asked the cloners of Kamino to help with that. The thing is, he ended up having another offspring the natural way anyway. It happened on a mission to Corellia, a bustling world where someone like Jango could blend in, not in complete anonymity like he enjoyed on Coruscant and also without the conspicuousness he invariably had on more tranquil worlds where he'd have to deprive himself of his distinctive Mandalorian armor, or even populations with established gangster elements like those under Hutt control, where he could operate openly.
No, on Corellia Jango fit in nicely, and he was immediately surprised by that. It put him off-guard. He was there long enough where one of the locals succeeded in seducing him. Imagine that! She'd been fascinated, not frightened, by him.
He didn't know anything about what resulted from those sultry nights until the day the young Han Solo introduced himself to Boba, who later went and told him about it. At first Jango dismissed it as a case of boys being boys, who tended to hero-worship him without discerning or worrying about what he did for a living. But Solo was persistent and resourceful, showing up on other occasions and far outside the Corellian system. It was enough to convince Jango to take the matter seriously and investigate the claim.
It turned out to be true, of course.
By the time of his death on Geonosis, Jango had managed to forget all about the matter, however. The army the cloners had created from his genetic material had finally been made public, and it was a spectacle that eclipsed even his own concerns. It was his son Boba who watched Jango die. Solo was nowhere to be seen.
But Solo hadn't forgotten. As the years advanced he became increasingly bitter, although he presented himself as jaded and flippant, thinking more about himself than anyone else. He was careful to travel in the same circles as Boba, and so that was how he became a smuggler for Jabba the Hutt. He clearly never got over the fact that it was Boba who was the acknowledged child of the great Jango Fett, and held a burning grudge against him.
It might also have been the reverse, by the way. These matters aren't especially clear. Both Boba and Solo led difficult lives to follow. It might have been that Jango rejected the known son in favor of the tantalizing mystery, the living proof of the life he could have led, one with more choices, more freedom.
The end result was the same. Boba and Solo became rivals, although more to the point mortal adversaries. It was Boba who tipped off the Empire to the fact that Solo smuggled for a living. This wouldn't have meant anything to the Empire except Boba happened to have a working relationship with it, and so his problems were its problems. In the end, Solo had no choice but to consider the radical alternative, which is to say the Rebellion.
It was Boba, once again, who convinced Darth Vader to lay a trap at Cloud City, which became the moment Vader finally revealed the truth to his own son, Luke Skywalker. Because of their obsession with matters of family, Boba and Solo forced many things to come to a head. It was Solo's activities that pressured Princess Leia to reveal her hand in the first place and therefore once and for all declare her allegiance to the Rebellion. It was Boba's activities that led Captain Antilles to bring his two droids, R2-D2 and C-3PO, with him into space (there was a time when droids were big business for people like Boba, or perhaps you'll know Jawa interests in that regard better? especially after they came into short supply after the Trade Federation and Techo Union reduced their interests in that regard). And of course, it was this whole episode that forced Lando Calrissian to finally declare his allegiance, too.
Lando was a friend of Solo's, by the way.
The saga of the brothers ended on Tatooine. Jabba had somehow managed to take Solo, Leia, and Skywalker as prisoner, and was set to execute at least two of them. The popular theory goes that it was the R2 unit along with Calrissian and Leia who saved the day, but it was actually the Wookiee Chewbacca, another of Solo's friends, who was responsible. The thing Solo had learned early on was that he needed advantages, like allies. He spent his life making them, but he usually left them strategically placed around the galaxy like assets, which was what he did with Calrissian, for example. Chewie was different. Chewie was constantly at Solo's side, and the first one he saw after being freed of the carbonite Boba and Vader had frozen him in at Cloud City. (Okay, so the first was technically Leia, who was actually the strongest link he had to his father, if you think about it.) There had been a whole scheme put into place, which was why they had all traveled to Jabba's palace to begin with, how they had become prisoners.
During the daring escape, the trap was sprung and chaos immediately erupted. Only Chewie knew the depth of the rivalry Solo had with Boba. He understood how complicated the emotions were, too. Neither could handle a drawn-out goodbye, if such a thing were even possible. That was how the Wookiee ended up guiding Skywalker into "accidentally" doing the deed for Solo.
Some things are just perfect like that, messy but perfect. Also, things like family. It was only in this way that Solo finally made peace with his father. Now he truly understood how Jango had led his life all along.