It indicates a consequence or result, meaning "from this" or "for this reason."
Here are some examples:
* It was raining heavily, hence we stayed indoors. (meaning: because of the rain, we stayed indoors)
* She worked hard, hence she got promoted. (meaning: as a result of working hard, she got promoted)
* The team was tired, hence they lost the game. (meaning: due to fatigue, they lost the game)