Emergence
Also said as Emergent gameplay, Emergent behaviour
Behaviour that nobody wrote, arising from a few simple rules interacting. The game's designers can be as surprised by it as anyone.
It gets you far more play than you authored, and players take it personally because they found it themselves. It can't be fully tested and may go somewhere you didn't want, so you steer it by tuning rules, not by writing outcomes.
Say it
“Stop scripting the fire. Give objects a burn rule and a heat value, and let it spread by itself. I want players to find uses for it that we didn't plan.”
Where you’ve seen it
Dwarf Fortress players found cats dying in taverns: cats walked through spilled alcohol, licked their paws clean, and got drunk. No one designed it: separate rules for spills, grooming and getting drunk did it together.
Not to be confused with random
Randomness is unpredictable because a die says so. Emergence is unpredictable because the rules are too tangled to foresee, and it does the same thing every time from the same start.