$ParentLink is the MathLink LinkObject currently used for input and output by the Mathematica kernel in a particular session.
When the Mathematica kernel is started by a Mathematica front end, $ParentLink gives the MathLink connection between the front end and the kernel.
You can reset $ParentLink in the middle of a Mathematica session to connect the kernel to a different front end.
See The Mathematica Book: Section 2.12.8.
See also: $CurrentLink, Links, $Input.