You're going to have to speak to me like I'm twelve, or I'm not going to be able to respond to this as well as I'd like to.
GIRLS! VIDEO GAMES! PUBERTY OH NO!

Let me try again down below going back to examples.
Heh. If that's a simple concept, that sure wasn't a simple way of describing it. Maybe:
"If the DM assures the player that they'll be playing by the rules, but ignores the rules, having everything happen just the way he intended beforehand, /and/ gets away with the deception, that's 'Illusionism?'" Close, Manbearcat?
Yeah, unfortunately I don't possess the brilliance of Feynman. My ability to capture difficult concepts in a few words is quite limited. I do my best but I usually turn into King Caveat, trying to foresee possible misunderstandings three conversations down the line. Oh well.
The above is pretty good. But I would sub rules (because it sort of implies just PC build + resolution mechanics) for system. That would encapsulate techniques (fudging or using fail-forward when the system doesn't advocate for it or expressly forbids it) and agenda (play to find out what happens vs run through the metaplot of an AP) along with rules. If rules means all of those things to you though, then rules is good to go. It just needs to be broad enough.
And all that stuff needs to mesh coherently. For instance, you can't cite
player agency or "play to find out what happens" as imperatives of your play agenda when you deploy duplicitous techniques which clash with, or outright upend, those tenets.
On with that example. Ok, let us go back to AD&D again and the Find Natural Shelter mechanics. When I was young, I liked to sit in on various GMs' games to observe their craft (rather than play) so I can "learn from the pros" and hone my own craft. This is my best recollection (should be spot on) of one of those anecdotes. Hopefully it highlights illusionism.
Players collectively: "Oh man, the ruins have to be somewhere on this mountain. I've still got most of my HPs. Lets push on and can camp inside there. There should be less chance of random encounters, we can have a defensible camp and get out of this downpour."
"But I've burned almost all of my spells at this point. That last combat with those wyverns ate up 2 of my last 4! If we don't find it real soon, we'll be in trouble!"
<More deliberating over pushing on or seeking a shelter for the night to rest and recover. The Fighter loses the argument and the players decide seek shelter and declare that action to the GM.>
GM: Alright, it will take 3 turns to try to find shelter, but you've got a pretty good chance. <reveals to them it is 40 %> There aren't a whole lot of monsters left on this mountain...but remember the legend that this place is founded upon? The cabal of wizards whose ruins you're seeking trapped this mountain with all kinds or protective glyphs...and their "twisted experiments" were set free in the cataclysm that claimed them. You haven't run into either of those yet!
<Now he doesn't tell them the frequency with which he is checking for random encounters, but I know. It is once every 3 turns.>
Fighter Player: Hey, I've got mountaineering. That should help us Find a Natural Shelter, shouldn't it?
<Now the rules are utterly silent on when/how/and to what effect the Mountaineering skill might interface with the Find Natural Shelter conflict resolution mechanics. However, after some negotiation between player and GM, it is agreed that if he rolls a success, the GM will add an extra 10 % to the chance, taking it to 50 %. It was negotiated to be Wisdom - 1, or something, because mountaineering doesn't have a check/AS associated with it. Up to this point, this all seemed to be sensible to me and was obviously above board.>
Fighter rolls below his Wisdom - 1. So now Find Natural Shelter is a 50 % chance....allegedly.
GM: Rolls behind the screen for a random encounter for the 3 turns of exploration. Now he rolls behind the screen for Find Natural Shelter. The percentile dice came up as 42 (pretty sure...it was in the 40s so it doesn't much matter). That should mean that they have now Found Natural Shelter and can rest and recover with no further exploration and a massively reduced random encounter threat.
Except no. He narrates the resolution pretty well and portends some ominous signs of lurking abominations...but also no secured shelter.
Players: Bummed but decide to give it a go again. This time the Fighter fails his mountaineering check, a saving throw versus petrification is made for loosed rocks during an ascent. Fighter actually fails and loses a few HPs for his trouble.
GM: Now it is time to check for the 1 in 3 turn random encounter. Rolls behind screen. Again, this fails to yield a random encounter. Except no. GM ignores the dice again and fakes rolling on his random table and goes straight to this abomination encounter that he had planned with the aforementioned twisted experiments.
He then fudged rolls (and probably HPs...I couldn't keep track of that...but it seemed like it) on the encounter with the abominations in order to avoid a TPK.
When I asked him about this after the session, he came up with classic illusionism justification (his idea of what would be fun and what would keep his players fearful, paranoid, and on the edge of their seats)...and then told me not to tell his players.
Player agency has been subordinated entirely to covert GM force. There are several issues at work here:
* Because the rules are silent on mountaineering's impact on the conflict resolution mechanics of Find a Natural Shelter (incoherent with the system's own resolution mechanics which they should interface directly with...AD&D was rife with this), we've got a negotiated roll for mountaineering's effect. Except there is no effect because the GM doesn't honor one or both of the Find a Natural Shelter resolution mechanics or the Fighter's well earned augment.
* Worse yet, we find out that there is actually
ONLY a penalty for the Fighter player declaring an action to augment the FaNS check. When he fails the second time around, he actually loses HPs.
* Finally, the GM fudges the 2nd random encounter roll, then determines via fiat (rather than resolving on the table) that it is going to be this uber nasty encounter with these arcane abominations from the wizard cabal ruins.
This is all with a group (1) already on the ropes resource-wise, (2) who have declared an action to FaNS rather than push on for the ruins, (3) who have risked fallout (and taken it) from an impromptu "ruling" that turns out to be all cost no benefit, (4) and then rightfully won an opportunity to FaNS again without another (any...but especially not a nasty one) encounter...but faced one, and a nasty one. The agency that the players thought they actually had to propel the fiction by the merits of their decision-making (and that decision-making interfacing with the fair application of the resolution mechanics) was utterly illusory.
Because the GM thought it would be fun and would keep his players fearful, paranoid, and on the edge of their seats.
Hopefully that helps.