Showing no emotion, acting as though nothing were unusual. For example, Richard ate the snails without batting an eye. A related phrase is not bat an eye, as in He didn't bat an eye when she told him he was being laid off. These expressions, which use bat in the sense of “blink,” date from about 1900.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.