My understanding of it isn't comprehensive, (I can dig through the CR, but we all miss things or misinterpret things.) But the clearest example of how it works would probably to illustrate it using (what I think is) a pretty cool commander,
Sharuum the HegemonSharuum as a General, was particularly weak to tuck effects before the rules change- because Sharuum is a General that frequently wants to litter your graveyard, or get stuck in your hand- because she has the hefty 6 mana cost upfront- which makes General tax sortof rough.
When I'm playing Sharuum, I find it disadvantageous to displace her when put underneath an
Oblivion Ring, so I simply let her hang out in exile until I feel like playing a proper piece of enchantment hate (allowing me to effectively summon her, and recur an artifact for the cost of the enchantment removal- swag.) This works, because she isn't forced into the command zone- and if the rules WERE like that, Generals who enjoy being in the Grave or Hand simply
wouldn't function (which, much like tucking a General- tends to go against the spirit of EDH.)
Most of the confusion regarding this probably comes from how people typically show "exiling" on a board, and display the Command Zone in a similar way (cards floating on the field, not in play- not in the discard pile.) Exile isn't the same thing as the CZ though (it's a "special zone".)
The way I like to imagine how it works, is that it's like operating a clutch while driving stick. When your Commander changes zones in a way that would put them into hand, library, graveyard, or exile- then you can choose to displace them to the CZ (effectively your "clutch" for the Commander being put out of reach.)
With Sharuum in mind, this means that I don't have to send her to the CZ if I want her in my Graveyard for
Trading Post or
Junk Diver shenanigans- but if an opponent chooses to blow a
Relic of Progenitus- when she shifts zones again, I get the chance to use the clutch- and put her back into reach. That's just sortof the idea of the command zone- it doesn't force the player the utilize it, but instead enables the player to always have their commander in reach while playing EDH.