An "inside option" is the bargaining offer a player can take.
An "outside option" is a payoff a player can get if bargaining fails. Here, in the context of interstate bargaining, the outside option is the player's payoff if the states go to war.
Generally, the better a player's outside offer is, the better the player's inside offer will be. The idea here is that the player making the offers has to give more to induce the receiver to accept.