Shepardize: To determine the subsequent history and treatment of (a case) by using a printed or computerized version of Shepard's Citations. Also, to check the precedential value of (a case) by means of shepardization (Black's Law Dictionary, Ninth Edition).
Shepardizing: "... to see if a case has been overturned, reaffirmed, questioned, or cited by later cases" (Wikipedia).
The American legal system is based on stare decisis, which is the "doctrine of precedent, under which a court must follow earlier judicial decisions when the same points arise again in litigation" (Black's Law Dictionary, Ninth Edition). Shepardizing determines if a particular court case has been overturned or overruled or reversed by a higher court, and thus becomes null and void.
NOTE: The Westlaw database employs a similar tool as Shepard's Citations called KeyCite. From the home screen of Westlaw, open the "Campus Help Guide" near the bottom of the screen for directions in using KeyCite
To get a sense of what it means when a court case is overturned, read through these famous Overturned Supreme Court Cases.