Verse - as related to show tunes or by extension jazz standards.
An introduction to a piece of music in standard form, usually sung out of time of with great freedom. Often used as a method of advancing plot in a musical before the sometimes out of context lyrical content of the tune.
Some well known examples include Lush Life, Some One to Watch Over Me, I'm Old Fashioned, and Bewitched, Bothered and Bewildered