Serial means arranged in a series. If you get a serial number with your new phone, that's a number assigned to the phone when it was made, to distinguish it from all the other phones.
Serial has nothing do to with breakfast (that's cereal). It means "in regular succession." If you make a deposit into your savings every week without fail, those are serial payments. You might not recognize grandma after her serial plastic surgeries. A serial killer kills multiple times in similar ways. If you publish a magazine that comes out periodically, you could call it a serial. And your favorite recurring show on TV is a serial too.