For example, if someone has never experienced poverty before, but then visits a developing country and sees firsthand the conditions that people live in, it might bring home to them the reality of poverty and make them understand it in a way that they had never understood it before.
The phrase can also be used to describe a situation where someone has to face the consequences of their actions in a personal way. For example, if someone has been driving recklessly and gets into a car accident, it might bring home to them the importance of driving safely.