When you make a delivery, you bring something somewhere. A delivery can be in the form of something physical, as when you receive a delivery in the mail, or verbal, as in the delivery of a speech or address.
Delivery once could only mean "the action of handing something to another," but it has a long history of being applied in other ways. The idea of childbirth as being a delivery came about in the 1570's, while the term was applied to a punch in the 1580's, and to throwing a ball in 1702. A verbal delivery is the manner in which a speech is presented. As a comedian, you know the importance of a good delivery — timing the punchline just right.