Daily copy is a daily transcript is provided by the court stenographer who is in court during the trial recording all the questions and all the answers that are given. A stenographer is also known as a court reporter. Their job is to record everything that is said in the courtroom during trial.
When an attorney asks the court reporter for "daily copy" they are literally asking for an expedited rush transcript of everything that was said that day. An attorney who purchases daily copy will be able to use that while cross examining witnesses as well as when preparing closing remarks.