Dual Trading

A broker trades on behalf of a client. That represents their main job. For them, trading for the client is just "trading." (Maybe we'll call that "mono trading." On second thought, nah, we'll just go with "trading.")

"Dual Trading" comes in when the broker trades for herself at the same time.

So, Bruno Funnycoat is your broker. You tell him to buy you 500 shares of Mass Quantities Inc. He fulfills that order, but at the same time, picks up 300 shares of Mass Quantities for himself. Bruno is trading for you and for himself at the same time. Dual trading.