Level Editor is a feature in the Steam version of Super Meat Boy, it allows you to create your own levels and post them to Super Meat World.
-Update: you can still create levels in the Level Editor but you cannot upload them to Super Meat World.
You may use the tilesets of every chapter except Cotton Alley in Super Meat Boy. Every character is playable in your level without having to unlock them.
Video Tutorial Edit
This is a six part video tutorial by Edmund McMillen (souldescen)