The meaning of the phrase drop of a hat is immediately. If you do something at the drop of a hat, you do it immediately (without any delay) without stopping to think about it.
Drop of a Hat is an idiom. What is an idiom?
"An idiom is a phrase that is common to a certain population. It is typically figurative and usually is not understandable based solely on the words within the phrase."
"When you use the expression 'At the Drop of a Hat' you mean that something is happening instantly, without any delay." For example- We're all packed and ready to go; we can leave at the drop of a hat.
