To display a subtle emotional reaction, such as consternation, annoyance, sadness, joy, etc. Generally used in the negative to denote that the person in question did not display even a hint of an emotional response. Mary didn't even bat an eyelash when I told her I was moving out. That guy is dangerous. I heard he killed a man without batting an eyelash.

To not display even a hint of an emotional response, such as consternation, annoyance, sadness, joy, etc. Mary didn't even bat an eyelash when I told her I was moving out. That guy is dangerous. I heard he killed a man without batting an eyelash.