Let's pick up the pace!
No, an Italian run doesn't refer to the Rome Marathon. It's a colorful way of saying speed through, a rehearsal in which the actors deliver their lines and perform the action at a much faster rate. Also called an Italian rehearsal or a Russian run, it's typically employed to help combat slow or dragging pacing, especially in comedies.
Many actors say it also improves line and cue memorization. Though some believe the term came out of the Commedia dell'arte scene, others claim it was inspired by the breakneck rehearsal schedule of 19th-century Italian opera companies. But then where do the Russians come in? As is the case with so many theatre expressions, its etymology is murky. Thankfully its definition is straightforward.
--- Raven Snook