To come eagerly and enthusiastically, typically in response to some enticement. Without fail, if I bring in doughnuts to the office, everyone comes running. The kids don't exactly come running when it's time to do chores around the house.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
come ˈrunningbe pleased to do what somebody wants: He expects his wife to come running every time he wants something.
Farlex Partner Idioms Dictionary © Farlex 2017