What is the role of "Parameter ID" in the user profile ?

Parameter IDs are a list of parameters that can stored in memory for a particular login. It can be used in multiple ways. One common use of it is to store commonly used fields in screens to be prefilled based on user preferences. Not all fields in SAP screens have a parameter ID.
[su3]>parameters tab

The correct parameter ID of a field in the SAP screen can be picked up as follows.
Whether a field in SAP is displayed based on the parameter ID of the user settings is based on the screenpainter settings of that screen. If the field is set to display the parameter ID , then it is displayed based on the settings in the user profile.