Now that git has become the standard version control software, which is used by software developers.
Now for system engineering and system administration purposes it used to be an approach to just login and do something and remember it or even note it somewhere.
Some people tried to just use RCS or SCCS on the server to create a local repository for the version of a configuration file. Some thought might be needed, if this is OK, because in the processes of checking in a file, it might be temporarily unavailable or inconsistent, because RCS can modify files in the processes. Usually this is not a problem, but if these kinds of problems occur, they are kind of weird ot find and fix.
Today the approach has changed a lot. Virtualization and it has become possible to build up thousands of servers. Or even millions, if you go to companies like Google. Typically servers perform a specific task and another server is used for another specific task and since almost all are virtual, that is possible. Thus it become necessary to run and maintain thousands of servers and that means that things have to be done really efficiently.
An important approach is to automate a lot of things. This can be done for example using Ansible or Perl, Ruby or Python. Or combinations of these. Or there can be a cloud that supports a lot of features out of the box. And tools that automate certain tasks…
So in the end of the day, it is no longer the typical approach to login to a server and do certain things, but to work on some kind of master server, prepare things and then run them on multiple servers from there. So the scripts and configuration files are created on this master server and now it becomes perfectly natural to use git to check them in.
Another engineer can clone the repository and perform the same task on a new server, for example.
Also it is a good idea to create branches and work with the branch on a test server, until it looks good and them merge that to the main branch. Even tags and release numbers make sense in some environments.
Only one tiny difference: While software developers tend to use IDEs like IntelliJ IDEA, Eclipse, Visual Studio or editors like Atom or Emacs, system engineers tend to use vi. This has several advantages: First of all, it is installed on every Linux server (unless you create one and uninstall it to disprove this, of course), it runs well across an ssh session even with relatively slow internet connections and it is powerful once you learn how it works. So I recommend to learn just the basics to get simple stuff done. And I recommend to avoid heavy customizing of vi, because that might cause problems when working on a server without the customization.
And even though today work is done mostly on these master servers, of course it does still happen, that it becomes necessary to login to a specific server to check out if the stuff worked as desired or to do tiny tasks that have not been automated. But remember: Lazyness is good. You should hate doing repetitive work on multiple servers and figure out how to automate it, if it happens for the third time or if it can be anticipated that it will happen more often. Automation not only creates efficiency, it also allows for better collaboration (via git), better consistency and better stability. It is the way to go.