To my limited understanding Skyrim Mods are basically a form of hacking into the game's programming and modifying it in a way that it was not meant to be played or viewed.
There's no "hacking" involved if a mod is properly made, unually with the Creation Kit which is essentially the same tool Bethesda uses to create the game and DLCs. Technically, there's no difference between a Bethesda made DLC and a mod other than the fact that DLCs are official and made by Beth while mods are not. Mods are additives, allowing one to add to, take away from, or augment/customize the game however one sees fit, affording the PC version the game extra elasticity.
If I change my desktop wallpaper to an M.C. Escher drawing, does that qualify as something Microsoft/Apple "never intended"?
I'd assume this can only be done on PC versions of the game, but could someone please elaborate on this? Are my thoughts accurate?
Correct. While many mods would run without issues on the consoles, provided MS/Sony allowed 'em, there are many mods which would add too much overhead given modders, aptly, aren't as restricted when it comes to resource consumption given PCs tend to have much more RAM, VRAM, PCU power under their hoods. There are, evidently, ways to use mods on consoles, however not without breaking MS'/Sony's EULA, thus discussion of such is not permitted here.
Cheap and sometimes decent alterations to gameplay.
Just like with
any creative medium (whether officially made or not), there are hits and there are misses.