A leveled list is a list of items or creatures that are going to pop up in your game when your character reaches a certain level. This aids in maintaining a somewhat consistent level of balance in the game as your character levels up.
For example: Say you are making a dungeon. You add a whole bunch of skeevers in it. If the player is at level 1 and enters the dungeon with a dagger, the player is in for a fight. If the player enters same the dungeon at level 35 wearing glass armor and wielding an ebony axe, the player wouldn't even have to fight going through the dungeon, because the skeevers are not going to be able to make much damage. heck, you could even wear the ebony mail and kill them all without landing a blow

So, how do you prevent that? With a leveled list. Rather than just adding skeevers to your dungeon, you create a leveled list with as many creatures as you think is necessary, and assign them the level in which they are going to appear. So, following the dungeon example, you could create a LeveledCharacter list with the following:
1 skeever
5 wolf
10 bandit
15 bear
20 spriggan
What does that mean? It means that if the player enters the dungeon while at level 1 but at less than 5, the player is going to face a skeever. If the player enters the dungeon at level 5 but less than 10, the player is going to face a wolf. If the player enters the dungeon at level 10 but less than 15, the player is going to face a bandit... and so on.
The same logic applies to item lists: you usually don't want the player to open a chest and find ebony armor and weapons at level 1 and make the game a cakewalk, nor face an enemy wearing ebony armor and wielding an enchanted ebony sword when you are level 1.