Archiving an employee means that user will no longer be able to sign in and use TSheets. Even though an employee is archived, TSheets saves the associated data. The only information "cleared" upon archival are any personalized settings like time off or overtime settings. These would need to be reset up if the employee was reactivated, and they would need to be re-invited to the account.
As an admin or a manager, you will still be able to see all of the archived employee's timesheets and their data will still appear on reports, but the timesheets cannot be adjusted after they are archived.
To archive an employee, see: How to Remove (Archive) Employees.
If after archiving the employee you find that you need to reactivate them (to edit a timesheet, if they're a seasonal worker, etc.), see: How to Reactivate Archived Employees.