It's not a new word. In fact I would say it has largely fallen out of common use. I wouldn't quite say that it's archaic...more just a little unfashionable/uncool...and maybe more literary. It feels like it mostly belongs in quaint Golden Era detective mysteries and, at least to me, it feels more British than American. Arrest or catch are decent substitutes (though arrest is used to describe a more specific judicial action generally done by police.).

When you "nab" someone, imagine picking up a doll out of a scene or catching a pen before it rolls off the table. It is like "catch" but more "caught in the nick of time."

The word "nab' has been around for a long time. One dictionary mentions the 1600's. It is an informal expression. It means, as you said, to apprehend, as police would do with a criminal during an arrest. The second meaning is to suddenly seize, take or snatch. One of my older dictionaries says it probably came from Scandinavian, Norwegian or Swedish words, such as nappa, which also means to snatch. It is definitely still in use in newspapers in both the UK and US but always implies a hasty, quick procedure, not a long stand-off.