To “Shepardize” a case or statute means to use a “citator” to find out which later cases, articles, etc. have discussed the case or statute at hand. This is done by using Shepard's on Lexis, KeyCite on Westlaw or BCite on Bloomberg Law.
Shepardizing is done for two reasons: 1) to see if your case is still good law, and 2) to find new cases on the same point of law.
For help using the online citators (you must be signed on for each service to access the tutorials):