A private listing as we call them here in DC or a pocket listing as they are generally called are off-market listings where the seller doesn’t want the world to know about the property.
They especially don’t want the websites like Zillow publishing all the details online.
And you ask, why would a seller not want to announce to the world they are selling?
Some reasons could be there is a divorce, or health or financial change, maybe it was already listed, or they haven’t done the necessary repairs, the seller could have a home full of valuables or they are a person in the public spotlight, and they want the sale to be handled with discretion and privacy.
I will do private listings but the more buyers who know about your home the better you will do.