Like many things in politics, it’s basically a minor crime blown up for political reasons. There’s also a lot of conspiracies around Hunter Biden (and some extend to Joe as well), some stemming from his work with Burisma.
That being said, in the midst of a shit ton of politically motivated investigations, it turns out they found that he did lie on his taxes and lied about owning a gun. He was convicted of drug charges and not legally allowed to own a gun. He could go to jail for that, but probably not the tax part. Tax cheats routinely negotiate out of court settlements, which almost happened with Hunter, before a judge decided to block it (maybe for political reasons)
Edit: sorry, he was not convicted of drug charges, but laws prohibit users of some drugs from owning guns and he lied about his drug use to buy a gun (something I’m sure is pretty common given the prevalence of gun use and the opiate epidemic)