Archiving a team member means that user will no longer be able to sign in and use TSheets. Even though a team member 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 re-setup if the team member 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 team member's timesheets and their data will still appear on reports, but the timesheets cannot be adjusted after they are archived.
To archive a team member, see: How to archive team members.
If after archiving the tea member you find that you need to reactivate them (to edit a timesheet, if they're a seasonal worker, etc.), see: How to reactivate archived team members.