Slice Processors are special scriptable assets that allow you to perform additional operations on a per slice basis. While there are a few default Slice Processors included, it is very common for custom processors to be needed on a per project basis. It is also common to need to create them to support third party tools. As such, processors generally require advanced scripting (and sometimes shader) knowledge.
Each processor is executed in the same order that the processors appear in the array. This allows you to chain together processors if you wish, running code in one processor that relies on code from an earlier processor having been run.
It is your responsibility to ensure all changes made by your processors are lasting. Changes made to game object or component settings may need to be made with SerializedObjects and SerializedProperties.
It should be noted, however, that the execution of the processors occurs before each game object slice is turned into prefabs, so any changes made should be saved to the prefab asset (assuming you are creating prefabs).