When you do something bad, it makes people lose respect for you. It might also make people lose respect for people who are connected to you, like your parents, your boss, your coworkers, or even your entire country. To describe this, we say that your actions "reflect badly on ___":
Scandals like these reflect very badly on the current administration.
You're only thinking about yourself. Did you ever stop to consider that it reflects badly on us as well?
You can also say that an action "reflects well on" something. For example, the principal of a school might say this in a speech to the students:
We're here to do everything we can to help you achieve, because when you accomplish great things, that also reflects well on us.