X11 is the main graphics rendering system in the linux universe. One day it may be replaced by ‘Wayland’ – that’s the name of the system that is meant to be its replacement.
Ninety-nine percent of graphical applications in linux need to communicate with an X11 system in order to render windows.
In X11, the client/server relationship is a little unintuitive: your local machine has access to your graphics hardware (GPU+Monitor), and so it acts as a ‘server’, allowing ‘clients’ to connect and make use of your screen. So, when you connect to a remote system, you will need an X11 ‘server’ which will allow connections from ‘client’ applications running on the remote system.
This will allow you to run graphical applications on a remote machine, and have the interface (window and buttons, etc.) render on the computer in front of you.