Off the cuff

 
Off the cuff means not prepared in advance; impromptu; or extemporaneous. It can also mean informal or casual.

"His off the cuff remarks got him into trouble."
One site quotes the origins of this phrase as being 'back in olden times' when people who borrowed money had the debt written down on the lenders cuff in the absence of a formal contract. That seems unlikely to me, even in days when washing one's linen was not carried out quite so punctiliously as it is nowadays. (I later discovered that the phrase 'on the cuff' is slang for 'on credit' but I still have doubts about its orogins.)

I should have thought a far more likely origin for off the cff was the idea of a person using his cuff on which to make some basic notes for a speech. He would then refer to these notes during the speech which, rather than being read out in a prepared manner, simply covered the main points off the cuff. The term seems to have entered the English language around the 1940s.