A dry run is a rehearsal. The term appears to come from American firefighting jargon, where dry denoted a practice where the hoses were not turned on. Here is this detailed description of a dry run from the Frederick, Maryland News of 28 May 1901:
Not less than fifteen or more than seventeen men to each company. Dry run, standing start, each team to be allowed one trial; cart to carry 250 feet of hose, in 50-foot lengths; distance, 200 yards to hydrant, attach and lay one line of hose 150 feet from hydrant, break coupling and put on pipe,...ready for water. (source)
The phrase today applies to anything that needs to be rehearsed.