X is a display server for unix-like kernels and operating systems. A display server is a program that runs while other programs (client) send data to the server, and the server puts that data on the screen. X clients are usually organized into boxes called windows (which is actually the namesake of Microsoft Windows) and they cannot be manipulated all on their own. They need software known as a window manager or WM to provide controls to move around, resize, and close windows.
X, despite some considering it being essential software for users of the Linux kernel, is actually not part of the GNU suite of software due to it's licensing having conflicting clauses with GNU's license.