It can be used in a few different ways:
* To introduce a serious topic: "We've been joking around, but on a serious note, I think we need to address this issue."
* To emphasize the importance of something: "On a serious note, this project is crucial to our future."
* To acknowledge that a previous topic was lighthearted and now it's time to be more formal: "On a serious note, I need to talk to you about something important."
Essentially, it's a way to tell the listener, "I'm about to say something that needs your full attention and serious consideration."