Permissions determine which users can access which functions of WorkLogPRO. Don't forget that JIRA's own settings and permissions may also affect functionality of the add-on. For example if you disable time tracking of JIRA, WorkLogPRO doesn't work.
Permissions specific to WorklogPRO can be accessed through the selected Project's own settings menu under Time tracking permissions at the bottom of the permissions list. You may refer to Managing Project Permissions page in Jira user manual to understand how permission management works.
There are two different permission sets for WorklogPRO, "Project Permissions" and "Global Permissions"
View Own Worklogs: Gives permission to only view worklogs that are created by the users themselves. You also need "Browse Project" permission because without it you can't view the issue. To able to view worklogs of an issue, you need permission to view issue in the first place.
View All Worklogs: Gives permission to view worklogs that are registered by other users.
View Worklogs of Private Issues: You can mark some issues as "Private" using "Issues" configuration page of WorklogPRO. Worklogs of those issues are only visible to worklog author and worklog update author if work is registered by someone else in the name of worklog author. Using this permission you can give this permission to other users to. This is generally used to handle more personal worklogs like "sick leaves".
Work On Issues: Allow users to create worklogs on the issues.
Log Work for Others: Allows users to register worklogs for other users. You also need to "Edit All Worklogs" permission to create new worklogs for other users too. This is used to mark all worklogs created by a 3rd user as "Edited" worklog on the user interface.
Work on Uneditable Issues: Normally you can't log work for non-editable issues either using Jira's own 'Log Work' window or WorklogPRO's 'Log Work' window. This is determined by "jira.issue.editable=false" property of workflow status and usually this property exist for Resolved/Done/Closed status of issues and may exist on other workflow statuses as well. WorklogPRO allows you to override this behavior using this permission.
Edit Own Worklogs: Allows users to edit their own worklogs.
Edit All Worklogs: Allow users to edit all worklogs even if worklog is created by another user.
Delete Own Worklogs: Allow users to delete their own worklogs.
Delete All Worklogs: Allow users to delete all worklogs even if worklog is created by another user.
Approve Timesheets: Allow users to approve timesheets for the project.
Use WorklogPRO: Ability to use WorklogPRO. All of WorklogPRO functionality will only be available for these users.
Require Timesheet Approval: Allow users to submit their timesheet for approval. If a user is not covered with this permission schema, he/she doesn't need to submit their timesheet and related action will not be available on the Timesheet UI.
WorklogPRO Administrators: Allow users to modify most WorklogPRO global settings. Some features are still not available like scripts.