Indeed, it sounds like gibberish. Thankfully the CyanogenMod wiki
for each supported model is quite in-depth and explains the process in simple terms.
I had an old Galaxy Android phone. I wasn't keen on the Samsung bloat and the need for ODIN which only runs in Windows as you discovered. Samsung had their own app store in addition to the Play Store which looked like iTunes and invariably failed to update anything installed with it.
Motorola kept the bloat to an absolute minimum so it was near enough a Nexus experience. Even so, my 2013 phone is no longer supported so wasn't getting any more updates or security fixes and was stuck at 5.0.1.
That's why I switched to CyanogenMod nightlies. I ditched a load of rubbish bundled apps I never used from Google by using OpenGapps Nano (absolute minimum for play store and services to work) then adding only the ones I need. it is far more responsive, has better battery life and gets the monthly security updates. I've used it since Lollipop (CM12) and now run Marshmallow (CM13).
If Fedora did an ARM x86 OS with a phone compatible UI complete with dialer etc. it would be interesting to try it out. The only tablet in our house is a Kindle Fire HD 7" which was a present and gets used mostly as an eBook reader.