A dry run is a test or rehearsal for a public presentation or procedure. If you're nervous about your speech, you should do a dry run the day before in front of your family.
Stage actors do dry runs of plays in the form of dress rehearsals, in which they put on costumes and makeup and go through the entire show in preparation for opening night. Engineers do a different sort of dry run when they test vehicles or plane parts before they're used in real life situations. And you might take your new snowshoes on a dry run in your backyard before hitting the hiking trails.