What's the name of this thing? Inside part looks like a cheat sheet, but I have seen images with different content inside these "walls".
That would be the Dungeon Master's Screen. Sometimes referred to as a DM Shield, or Game Master's Screen (especially in non-D&D games), they are designed to give the Dungeon Master quick access to frequently referenced rules, and to obscure dice rolls the DM doesn't want to players to see.
They are usually filled cheat sheets to status conditions, more obscure but frequently referenced rules such as how much light a candle generates, or how protected a target is with cover, etc. They also sometimes come equipped with tools for quick generator of names, items, or even encounters!