A "pick up" is basically a "re-shooting", but not really a re-enactment. These pick ups are usually done after a taping, so as to not disturb the flow of the show.
I'll give a couple examples. During a taping of Card Sharks 2001 I saw, there was a moment when the players were introduced that they both embraced, for "good luck", however the producers felt this was not appropriate, so their introduction was re-shot, and this time they did not embrace.
Another example. During a taping of Bergeron HS that I saw, Jack Hanna had a skunk in his square. Tom made some comment about a "smell" in the studio. Well, I guess the producers didn't like that, and they had Tom reshoot his intro of the skunk.
Rich Fields also does "pick ups" of product descriptions for various reasons, whether it's audio problems, stumbling with a description, or perhaps inappropriate audience reaction (this was done all the time when they had "Zim's Crack Creme"... I watched Randy do a pick up of that, and I nearly cracked up hearing the description! Thank goodness I didn't screw him up!!)