A house show, also known as a live event, is a non-televised event that wrestling promotions hold aside from other regular shows. For example, the WWE has televised live events weekly, Smackdown Live and Monday Night Raw. They then hold house shows to continue to promote their superstars and stories for the remainder of the week. These events are typically held at smaller venues for less people than any televised event. And they can use this time to try out new gimmicks or season new talent before having them on TV.
A house show is similar to a dark match in that they are both non-televised. A dark match differs in that it is held before or after an event that was being televised.
To read more about dark matches, see my post about them here.