Meaning: Willing to do something immediately. At any moment; without persuasion, very promptly.
For Example:
1- He gets mad at the drop of a hat.
2- He used to be an actor. He tells stories of the old days at the drop of a hat to anyone who'll listen.
3- She still loves him, you know. Even now, if he needs anything she's there at the drop of a hat.
Meaning in Arabic:
في أي لحظة و على الفور