The DISPLAY:= variable

I saw a script that included the following:

   #!/bin/bash
   if test ${DISPLAY:=}x = "x" ; then
     DISPLAY="mymachine:1.0"
     export DISPLAY
   fi

Now if the variable DISPLAY:= doesn't exist, or is an empty string,
then the above test is true.

But what's the point of the test?  It must be an X-Windows thing (or
kludge?) that in some way uses the DISPLAY:= (not the DISPLAY)
variable.
   === Al