Superman is an alien. The kind of alien he is can hold their breath for a very long time. That means he can travel in space without having to breathe until he runs out of the air in his lungs.
The reason he doesn't just take every fight to space is because he's a hero, and he tries very hard not to kill the people he fights. So he only takes the villains that will survive up there.
That's the proper eli5 version that is likely what a kid would want to know.
But there is a good bit of lore behind it. Superman's breath holding ability has changed over time. Originally, it was only enough for short trips without breathing. Afaik, that was the case until after he died and came back, in comics. I don't think the Reeve movies really showed enough of that part of his power set to have an answer in that universe.
After he died and came back, a lot of lore was covered regarding why he could come back, and his unique solar based physiology became the default explanation for all of his powers. They expanded most of his power set as he recovered from resurrection. Instead of it being less than an hour or so, he started being able to go for hours. Iirc, that was enough to get him anywhere in the solar system without supplemental oxygen.
Over time, the explanation expanded to include the idea that he uses oxygen in his metabolism when it's available, and will default to it because it's more efficient than using solar energy to fuel his life processes. He is not (again, afaik, I haven't read his comics in a few years, and the current DC movie universe is vague) able to solely survive from sunlight alone.
I think he's currently not able to just straight fly to another star system, but can be in space for extended time, days to a week or two. As always, he's as powerful as he needs to be for the story, but long trips have generally shown him using a rebreather or some other type of air source. I can't remember the details, but he spends some extended time in space here and there after they introduced a son for him.
But, the part about why he doesn't just take fights to space as the default in universe is that he wouldn't just kill someone. Most of who he fights would die in space, so he only does that if the enemy can take it. Otherwise, why stop at space? Just take things into the sun, since some versions have him able to survive there.
The out-of-universe reason for comics is that space fights are boring in that format. Or at least that's what Didio said at a comic convention I went to ages ago when asked why they didn't take more fights off planet. Drawing panels for a fight is already a very specific art form. The kind of dynamic indicators to show movement as more than just a stillframe shot, giving that sense of action is what makes the great comic artist great
Doing that in space, with no background to help other than that earth and moon gets repetitive in a way that different buildings doesn't. All you can really do is show one or the other getting bigger/smaller in perspective. So it tends to be used to show how powerful a character is that they can fight in space, but then they go back to earth/planetary surface so it can be drawn more interesting.
And it doesn't take much hand waving. Why are the characters fighting? The typical reason is that the villain has a goal, and if the goal wasn't on earth, why would they bother landing in the first place? The story is going to have them at least trying to get down to the surface, no hand waving needed.
Space fights in animation and film are less constrained, and they do it more. They still run into trouble needing to show motion and perspective, but just the ability to have stars in the background makes it work. Look at the scenes in Invincible that are roughly the same in print and the show. Like with Allen first fighting Mark, the scene is handled slightly differently in each.
The usual caveat: I can't be arsed to treat lemmy like a school essay with citations, so I'm working from memory and that means flaws in detail.
