Final Fantasy games that use random encounters on a world map use divisions to separate where certain sets of encounters are fought. Many of the earlier games divide the map into a grid of squares of equal size. Depending on the location on the grid the player traversing the world map is standing on, different enemies will be encountered. Sometimes, due to a programming oversight, grid squares with encounters designed for one area overlap with land from another area. This often allows monsters intended to be fought when the party reaches a certain part or area in the story to be fought earlier. Many of these areas are in remote places where players have to go out of their way to reach. Players can exploit these areas to grind for experience and gil early.
The term Peninsula of Power was coined in an issue of Nintendo Power for the original Final Fantasy, where it was hinted the area can be used for easy experience and gil. Players have continued to call such similar areas as the Peninsula of Power within the series and in other video games.
The Peninsula of Power is a peninsula northeast of Pravoka, accessible by ship. In the northernmost tip of the peninsula, monsters usually encountered in the Lufenia area are encountered there as well, allowing for early access of these monsters.
This occurs because the world map is divided into an eight-by-eight grid, each containing 32-by-32 squares. The grid determines which enemies are fought in any location. Where the most northwest grid-square is $ (0,0) $, from there to the east it will be $ (1,0) $ and to the south it will be $ (0,1) $; $ (6,4) $ contains Pravoka, and to the east is $ (7,4) $, the area south of the peninsula and including the southern part of the peninsula. $ (7,4) $, $ (7,5) $, and $ (6,5) $ all contain the same enemy formations not much tougher than Pravoka's.
However, the very northern tip of the peninsula infringes on the square that covers a large section of the area surrounding Lufenia including the town itself. In this square, $ (7,3) $, the enemies fought are built for the late stage of the game after the airship is obtained.
While not exactly a Peninsula of Power, in the NES version of Final Fantasy exists a short, 3 tiles-long area south of the mountains underneath the Yahnikurm Desert, consisting of only Goblins as enemies. This is caused by the same oversight, as these tiles are covered by square $ (5,3) $, the same square as the entrance of Matoya's Cave.
This area can be accessed right after Goldor Manor. From Amur, the player must fly north. The area does not look like a peninsula, but is the same concept as the Peninsula of Power from Final Fantasy. The grid ends one tile after the mountainside, and this horizontal strip of land contains monsters from around the Crystal Tower area, which are monsters intended to be fought near the end of the game. This area does not apply to the 3D versions.
The monsters fought north of Mt. Ordeals are those from the Mythril and Troia areas. The grid tries to cover all the islands north of Mt. Ordeals, but has been done poorly resulting in early access to stronger monsters. This is still available in the Final Fantasy IV: The Complete Collection version. This area does not apply to the 3D versions.
Similar to the other examples, but not quite a Peninsula of Power. In the World of Ruin, there is a peninsula with six trees directly east of Kefka's Tower; its random encounters are set to default resulting in encounters that solely involve Leaf Bunnies and Darkwinds, one of the first enemies fought in the game found right outside Narshe.