A duet team can choose to take different verses for each person and harmonize the chorus. They can choose to harmonize the entirety of the song and then not worry about who sings what since they are singing everything. Essentially a duet is just a singing partnership and an old school one at that, but it can mean so much more than that in a dream. Now when people sing in unison these days it is hardly formal enough to call a true duet.
If you have a dream in which you are doing a duet, this means that you are in a strong partnership with someone in your life and because it is going so well, the positive feelings from it are leaking into your dreams. You perform a duet with someone that you are extremely comfortable with, someone that you can really trust. Therefore if you have a dream in which you are performing a duet then this dream means that you are feeling quite comfortable with your stance in the world with this other person and with where your relationship is headed. Maybe you are just happy at having made a new friend and it is making you feel all giddy inside. Or maybe you have just talked to a girl that you really liked and got a positive response from her which made you feel like heaven. This is a good reason why you might be having a dream about a duet.