Okay, let's say that you have filed in an appeals court for a writ of mandamus, and you have won. The appeals court says that the trial judge or other governmental actor has to do what you told the appeals court that that person should have done. Will the appeals court issue an order for that actor to do what it told that actor to do? Almost certainly not!
Appeals courts often think that it is disrespectful to mandamused people-- elected officials, including trial judges-- to issue a written order to them like they were flunkies. So in their opinions they simply say what the order would be if it were issued. They then say that the the mandamus order will only issue if the official-- normally a trial judge-- does not correct the action on their own soon after the opinion. This is commonly called conditional issuance of the writ.
If an appeals court issues a writ of mandamus unconditionally, that means that it is angry at the ordered person. I remember having seen one, but I haven't found the case again yet.