A Nash equilibrium is a combination of strategies in which each player's choice is a best reply to the others', so no one can gain by unilaterally deviating. This makes it the only kind of agreement that is self-policing: it needs no external enforcement because everyone's incentives already align with keeping it.
In a game played across sequential moves, work out the rational choice at the final decision point first, then use that to fix the choice at the step before, and so on back to the start. Reasoning from the end backwards yields the subgame-perfect strategy and rules out threats that would be irrational to carry out.
In a one-shot Prisoner's Dilemma, defection dominates and rational players fail to cooperate; cooperation becomes individually rational only when the game is repeated indefinitely, so that future retaliation can deter present cheating. The possibility of ongoing reciprocity, not goodwill, is what sustains the cooperative outcome.
Many coordination games have several equilibria that are equally good as solutions, and nothing within the game itself picks one out. A convention is a shared expectation, often arbitrary and inherited from history, that tells everyone which equilibrium to aim for, which is why driving-side rules or focal points resolve coordination without debate.