When you say something off the cuff, you make it up on the spot, with no practice or planning. It's extremely difficult to give a speech off the cuff; it's better to prepare for it.
Making a wedding toast off the cuff is one thing, but presenting a college graduation speech or addressing an economists' convention off the cuff would be something else altogether. It can also be used as an adjective: "I think it sounds so much more sincere when the Academy Award winner gives an off the cuff speech, don't you?" This American English phrase comes from the idea of hastily writing speech notes on your shirt cuff instead of fully preparing.