From Monkey Island wiki
The Tri-Island Area is, broadly speaking, the area of the Caribbean in which a majority of the Monkey Island series takes place. The term is not used before The Curse of Monkey Island, when the Voodoo Lady mentions to Guybrush that Elaine is the governor of the entire "Tri-Island area, comprised of Mêlée, Booty, and Plunder Islands". However, the in-game map showing these three islands also includes other nearby islands, such as Phatt, Scabb and even Monkey Island, none of which are governed by Elaine.
In the next game, Escape from Monkey Island, the map is specifically labeled "Tri-Island Area", and includes yet more islands: Lucre, Pinchpenny, Spittle, and Jambalaya. On the other hand, Scabb, Skull and Blood Island have all been dropped from the map (and aren't depicted in the game).
The term gets used much more widely in this game: for instance, Lucre Island is identified as the largest urban center in the Tri-Island area, and Ozzie Mandrill's plan is to expose "every pirate in the Tri-Island area to the devastating affects of the Ultimate Insult". It is not made clear if Elaine is Governor of all these islands, or just the three identified in The Curse of Monkey Island. However, as Phatt Island has its own governor and Scabb Island is known to lack a government, one can assume this is unlikely. It can also be assumed that Blood and Skull Islands are not under the jurisdiction of the Governor; Blood Island is apparently lost from the shipping lanes and has a single resort built on it, while Skull Island is presided over by King André, the Smuggler's Cave being the only (seen) human habitation on the island.
The idea of the Tri-Island Area was introduced in the third game as a way of explaining how Elaine Marley could be simultaneously the governor of several islands, although Elaine is said to have resigned from her governing duties on Mêlée in Monkey Island 2: LeChuck's Revenge. The Tri-Island Area may have its counterpart in reality as the Tri-state Areas of the United States, points at which three States are connected. Due to the inclusion of several more islands in the fourth game, the Tri-Island Area seems to have lost its meaning syntactically, now referring to more than just the three main islands.