Also known as "schems", schematics are a part of WorldEdit which is an open-source plugin for Minecraft developed by sk89q.
Schematics allow you to easily save a selection on your clipboard to a file that you can move to another server or share with others online. Its great if you want only certain parts of a map to be used on another. Its also a great way to keep your prized creations safe from corruption.
While in game you can save, load, and list the avaliable schematics. In the video, I show you how :D
As for the "grid" thing. That's the WECUI and I have a video tutorial here. • How to Install the Minecraft WorldEdit Cli...