To ad-lib is to speak or act without a plan, in the moment. The script is gone, or you never had one, or something on stage went wrong and you have to keep going anyway. Actors ad-lib. People giving a speech ad-lib when they lose the next line, or when the room wants a warmer answer than the paper. Musicians do it too, though they more often say improvise. You can use it as a verb (she ad-libbed a joke) or as a noun (that line was an ad-lib). You will see ad-lib, ad lib, and sometimes adlib; the hyphen is common. It smells a little of theatre and comedy, and it is not very formal. Though actually, we stretch it a long way off the stage: a teacher with no slides, a host who throws away the cue cards, a friend who answers a hard question by just talking — English still lets you say they ad-libbed. It does not have to mean careless. Good performers practise so they can ad-lib well. It also does not mean the whole show was made up; often only a sentence or two is.