'at that very second' = at that precise moment, or at exactly that second in time. 'Very' effectively means 'exact', so when you use a phrase including 'very second' you are saying that it is a very accurate time.
October 6, 2008
'Very second'=immediately, nothing to do with tim
Like if your mom tells you, "Clean up your room this very second!" She means NOW not 5 seconds from now but NOW.
October 7, 2008
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