> Can you explain this? What are the exploits?
Traditional desktop Linux allows different apps to more-or-less freely communicate with each other (called the x11 protocol). This works really well for old apps (and admittedly not too bad for new ones) but is very slow and exposes a lot of bugs. On top of this, you have potential exploits in your filesystem from loosely permissioning important settings and identity files. So, the attack surface for a traditional Linux distro is relatively large.
> Is it the equivalent of running a .exe or .jar on windows, but with an extra layer of protection?
Kinda! Linux software is distributed as packages, which contains a binary (the exe/jar portion), a dependency manifest and whatever static content it needs. A sandbox like Flatpak will take those packages and put it into a sandbox, to prevent hostile interprocess communication and filesystem exploits.
None of these mitigations are perfect per-se (nor are they on Mac/Windows), so use them wisely if you intend to use them at all. I have used a non-sandboxed system to run old 90s Windows games for years though, and haven't picked up any significant issues. YMMV, it is Linux after all :P