It means, to swoon or faint. From when ladies wore corsets and would faint all the time, it was said they "caught the vapors", maybe from the night air.
"Catch, or Caught the vapors."

Bring the fainting couch Alfred, Bessie "Caught the Vapors" again! If he proposes, I will "catch the vapors", tout suit.
by steampunk-addie June 16, 2011
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