A house show or live event is a professional wrestling event produced by a major promotion that is not televised, though they can be recorded. Promotions use house shows mainly to cash in on the exposure that they and their wrestlers receive during televised events, as well as to test reactions to matches, wrestlers, and gimmicks that are being considered for the main televised programming.
House shows are often used to promote upcoming televised events, especially pay-per-views, and will then feature matches between wrestlers who are scheduled to work a match at the pay-per-view. This allows them to secure a 'feel' for each other's style and test out specific parts of matches planned for pay-per-view.
From the 1950s to late 1980s, most major matches and title changes happened at house shows, largely due to the costs to produce a TV show at the time, plus the lack of more modern technology making it significantly harder to tape a TV show. TV shows were taped in small studios, and featured squash matches, run-ins, and promos which revolved around feuds to be settled at the house show. Some of these big matches later aired, often scheduled "for TV time remaining", which usually ran out as the match built to a finish, hopefully making fans regret missing it and buy tickets to the next show. This changed in the 1990s as the formula for TV shows had changed completely by the time, largely due to the then-new Monday Night Raw produced by the World Wrestling Federation (today known as WWE) which changed the way TV shows were taped and proved to be a huge success for the WWF. And later with the advent of Monday Nitro.
House shows are similar to dark matches with both being untelevised events. The only difference is that dark matches are untelevised matches in TV programs which were already being televised.