Moogle Charm is a very rare gear item - equipping it on a character increases experience gain (only on that character) by 20%. As you can imagine, wearing that (or multiple of them - getting them will be explained in a separate chapter) can significantly decrease the time needed to gain higher levels, especially if you use other experience-increasing methods (like the Stacked Ham Sandwich described in a separate chapter).
Moogle Charm can only be acquired at fixed locations. One of the easiest ways to collect it is to visit one of the dungeons in the game - Daurell Caverns. Normally you will be visiting this location at the end of / just before completing the main storyline, as there are quite powerful enemies inside (like the 41 level Necromancer), although you don't have to fight the monsters to acquire the loot. You have to, however, be at least in chapter 3 to be able to access the area.
In order to get there, you have to drive through the tunnel in Schier Heights and find the stairs located near the road - the place on the map, as well as the stairs can be seen on the above screenshots. Run down the stairs, enter the route and continue walking along it until you reach the entrance to the cave. The cave is the Daurell Caverns dungeon mentioned in the previous paragraph. If you are here during the early stage of the game there's a high chance that your party will be severely underleveled and facing the enemies inside will be impossible. Just avoid any contact with the monsters lurking inside and if an encounter starts remember that you can run away from it by leaving the red circle visible on the mini-map.
Enter the cave and run down a little bit until you reach a crossing. Turn right and squeeze through a narrow passage. Continue your march (collecting numerous items along the way) until you reach an ice deposit and a cliff. Jump down twice to reach the lower floor and continue marching forward.
You will soon be passing a poisoned water reservoir and you will arrive at an open area, with routes leading left and right. Ignore both of those routes and look for a small island on the other side of the poisoned river, located directly in front of you - as seen on the above screenshot. There's an item located there - Moogle Charm you're looking for. Collect and equip it on one of the characters you want to get a 20% exp boost on.