This tool increases the priority of the work being done in an area. It can be used to build buildings in a certain order, used to make citizens gather resources first, or more importantly, used to make laborers immediately stop their tasks and attempt to put out fires.
When you drag an area with this tool, any pending tasks (such as building or collecting resources) that lie with in the area will appear red. Once you release the mouse button, your citizens will place these tasks at the top of their lists, and aim to complete them first - so long as you have the available resources, builders, or laborers.
One thing to bear in mind is that there is no visual feedback once you have used this tool - the areas turning red when dragging this tool will not stay red once you release it, even though they have been given the highest priority.
You can use the priority tool multiple times, and the most recent time will give the tasks the highest priority.