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The term was invented from a character in the Anime "Shin Chan", a mother who holds a stuffed bunny against the wall and punches it repeatedly in the gut to relieve her numerous frustrations.

The term is used to describe someone you know must be going home at night and punching some stuffed animal against the wall in secrecy.
"Shes little tightly strung, a real bunny puncher"

"I can't believe Gail remains so eerily pleasant, how does she do it?"
"I bet shes a bunny puncher!"
by UrbanPictionary December 21, 2007