Outcomes stabilize when no actor can benefit by unilateral change.
Nash's 1950 result, and the reason it matters is existence: every finite game has one in mixed strategies, so there is always something to solve for. Whether it is good for anyone is a separate question.
In practice
- Two firms in a price standoff both hold, because either moving alone is worse for the mover.
- A team's meeting culture is stable because no individual can shorten meetings unilaterally without appearing disengaged.