I think "what problems do they solve that I can't already solve" is the wrong way to look at it. After all, ultimately most language features are just syntactic sugar - you could implement for loops with goto, but it would be a lot less pleasant. I think that unions aren't strictly necessary, but they are a very pleasant to use way of differentiating between different, but related, types of value.
Ok. I'm just trying to understand what code I'm replacing with them. Like I wanna see the before and after in order to gain the same level of excitment as other people seem to have for them.
Often the explanations just seem rather abstract which makes it harder to appreciate the win, versus the hideous sort of code that might appear when they're misused.