I've got two legs from my hips to the ground And when I move them they walk around And when I lift them they climb the stairs And when I shave them they ain't got hairs!
In Urinetown The Musical, this is rather common, with examples including constant reminders that the Fax/Copy Girl's job involves faxing AND copying, and the secret hideout bearing a large, lit sign reading "SECRET HIDEOUT" - With the police pointing to the sign as evidence of how hard it is to find. But the all time winner has to be the reveal of The Twist:
Ms. Pennywise: Hope is my daughter!
Crowd: *small gasp*
Ms. Pennywise: AND I AM HER MOTHER!
Crowd: *HUGE gasp*
The Musical version of The Wedding Singer actually contains the lyric "People called him the wedding singer. He sang at weddings and so the name was apt."
Shakespeare's characters sometimes don the captain's braid, but often it's because of the limitations of the Elizabethan stage. To paraphrase another page on this wiki, if your actors are in the middle of a sword fight but they're only pretending to be using swords, it's probably helpful if the victim grabs at his chest and cries "O, I am slain!" so the audience knows what happened. Also, if your only set decoration is a big sign that says "Castle of Elsinore", the characters are going to have to provide a description of the castle in their dialogue if you want the audience to visualize it.
Plus, at the time only the playwrights themselves kept copies of the entire play; the actors were only given their own lines and the cues that came before them. Shakespeare was also rather stingy with stage directions, so the actors themselves needed the lines to know when their characters had died.