This sets the environment variable $DISPLAY to be :0.0. When you run an X-windows program, this tells the program where to find the X server, and which display on the X server to use.
The X server is the program that performs the actual tasks of drawing on the display and handling keyboard and pointer (mouse, tablet etc.) inputs.
You also don't need to export it: that just means that the setting will be inherited automatically from any programs that you run from the current shell. You could, for example, say:
DISPLAY=:0.0 xterm &
to just start an X terminal with DISPLAY set; any commands run on that terminal emulator would then have the DISPLAY variable available. In that case, the DISPLAY would be blank.
You can also change DISPLAY to run commands on other hosts, or other X servers. See the manuals for xauth and X.