We're not talking about breaking into computers. Hacking, in this context, is the process of editing the actual game, or ROM. That's why an edited game is called a ROM hack. And by edited I mean actually making your own levels and worlds.
I'm not going to go into detail here about how that's done, but if you really want to know, you can do a quick Google search on the topic. It doesn't take long to learn how to do it yourself, and nowadays there are YouTube tutorials for everything, so you'll be editing and playing your own hacks in no time.
I've been hacking Super Mario World since 2007 when I was 10. It used to be pretty popular on the Internet at that time. Of course, there weren't as many kids with knowledge about this kind of stuff, so it's been sort of a niche for me when I found out about it.
If you want just a quick glimpse at what some of my projects look like nowadays, here are a few screenshots. If you actually want to play them or make your own, I suggest you check with Google first. I've also made a very brief tutorial here if you want to look at that.