Git is a distributed revision control system with an emphasis on speed. Git was initially designed and developed by Linus Torvalds for Linux kernel development. Every Git working directory is a full-fledged repository with complete history and full revision tracking capabilities, not dependent on network access or a central server. Git's current software maintenance is overseen by Junio Hamano. Git is free software distributed under the terms of the GNU General Public License version 2.
The above summary is what Wikipedia says about Git. And it is all true.
Unfortunately, that description is very clinical. It's not going to help you understand why you should even bother with Git.
The short answer to why you should bother with Git, is that it helps you maintain a history of changes to your files. By maintaining a history, you can return to an earlier version of your file before "when everything just worked". This useful for all kinds of files, but is especially useful for files that provide instructions to a computer to implement the steps of a process you are documenting.
A longer answer to that question requires knowing a little more about what it means to document a process. You need to know how Git helps you with that work. You need to know the problems Git solves for you and how to get yourself out of a pickle when you find out your instructions are broken.
Most importantly, you need to be able to learn how to use Git along side your normal work. Get started with some basic commands and fix mistakes you discover along the way.
To answer why to use you want to use Git, read the the Git Primer.