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$DisplayFunction gives the default setting for the option DisplayFunction in graphics functions.
The initial setting of $DisplayFunction is Display[$Display,
$DisplayFunction is typically set to a procedure which performs the following: (1) open an output channel; (2) send a PostScript prolog to the output channel; (3) use Display to send PostScript graphics; (4) send PostScript epilog; (5) close the output channel and execute the external commands needed to produce actual display.
See the Mathematica book: Section 2.9.1.
See also: Display, Put, Run, $SoundDisplayFunction.
See the Further Examples for DisplayFunction.