Process Starter is a template-specific role you can give to users to allow them starting new processes from that template. These users are referred to as "Process Starters". Process Starters are different for each template: e.g. user may have permissions to start "Vacations Requests" but not "Purchase Requests".

To be able to change Process Starters for a specific template you should have permissions to edit this template. On a template editor screen you can use "Process Starters" option to edit the list of users granted the Process Starter role. 

Setting Process Starters to HR group, so that only members of HR group can start new processes from this template:

When user starts a new process she can see a list of all templates available to her, i.e. all templates where she has Process Starter role.

For example, if user has "Process Starter" role for "Vacation Request" template only - she can click on "Start process" button and on a Process start screen she will see only a "Vacation request" template.

Process start screen shows only templates available for starting a new process: