This isn't defending Bambu, and it's not an ELI5 because, whether you meant it sarcastically or not, the easy answer to your question is "you do not need to connect to a cloud service to use a 3D printer".
Bambu Labs however, has chosen to market their printers with an app that provides a "one-stop shop" for all things 3D-printer. You can browse their version of Thingiverse (or Printables or Cults 3D) and send jobs directly to your printer. You can also access your printer remotely (read outside your home network without tunnelling/port-forwarding/VPNs) to monitor prints, get notified when a print is done, get notified you've run out of filament, watch the printer work if it's equipped with a camera, etc. etc.
Bambu has been attempting to remove features that enable easy local (not-internet-connected) use cases and force everyone to use the cloud, etc. Or at least make it as painful as possible to skip the cloud.
Relevant context: X1C owner who did not update the firmware that forced bambu's "secure printing" workflow on users that previously used their local network "plugin".
I stopped using Handy, blocked the printer's access to the internet, and ultimately, did not miss a thing. The printer continued to work fine with my slicer of choice (softfever's fork of Bambu Lab studio's fork of Prusa Slicer's fork of slic3r, now known as OrcaSlicer).
Like most things these days, they make a decent printer, but are part of tech's steadfast march to control everything. The twist is that they're in a space defined very much by breaking control.