A live event that isn't televised. The bread and butter of wrestling's touring schedule. House shows are where wrestlers refine their in-ring work, experiment with new spots, and generally have more fun because there's less scripting and more freedom. The crowd is usually smaller but hotter because they're hardcore fans who paid specifically to see live wrestling. Storyline results at house shows don't usually affect TV continuity.
"He turned heel at a house show last night as a test run. If the reaction was good, they'll do it on Raw next week."