To catch and arrest someone. Often used in passive constructions. We'll be able to nab the perpetrator as soon as we have an eyewitness to the crime. I heard the serial killer was finally nabbed last night.

A thief. Used after another noun to indicate what the thief stole or some characteristic about the thief. Police are now on the lookout for the lawn-ornament nabber after a third house was hit last night. The pig nabber turned out to be a neighbor of the farmer, a mere boy of 15 who claims he was just having a bit of fun.