If you're not familiar with Cypher System (or Numenera and The Strange), GM Intrusions are basically "events" a GM can present to a player, along with 2 experience points. The player can accept the event, take 1 XP, and then give the other XP to another player. Alternatively, the player can decide that the intrusion messes life up too much, pay 1 XP from their pool (if they have it), and deny the intrusion.
On average, the system encourages the GM to get in one intrusion per session per player, not counting free intrusions, which are Cypher's version of fumbles on a natural 1.
It's a fascinating inversion on the idea of players having plot points or the ability to influence the story......and it lets players earn XP for increased struggle, and spend XP to make problems go away if it's really going to complicate their lives.
As an example, in last night's game I used intrusions like this:
Player rolled a 1, so I got a free intrusion and stated that the arrow missed the player but killed his horse, forcing him to make a speed defense roll to avoid damage from the crash.
I pushed a GMI on another player who was playing a Speaker and trying to distract the big bad (a rakshasa with revenge in mind). I gave him a GMI where if he accepted, his distraction attempt was too good, and the Rakshasa was now focused on capturing him instead of killing the other PC who had angered her.
Another GMI came up when one player asked an ambivalent NPC who may be a villain for help....the GMI was that she would accept the offer and help, but it would be her way (using her vile abilities to kill the enemies in question), but also spreading her nano-plague in the process. If the PC refused, then she might have offered some nominal (but not damaging) assistance.
Still yet another player was pushing to take out two enemies with daggers after vaulting over the barricade. I used a GMI to state that she succeeded in killing one, but the dagger snapped in his neck.
It's almost like a game within a game, to see what PCs are willing to accept in terms of twists in exchange for the XP. It also encourages me to be even more insidious and inventive with the GMIs, given I have already had a habit of doing something like this as part of the routine narration, anyway.
I've ordered copies of the Asset Deck and Intrusion Deck from Monte Cook Games, interested in seeing how I can put them to use next session.