The Security Password is an added safety feature. Ideally, only authorized payroll approvers should know this. It is first received via the sign up email from Sprout Payroll. Please note that this is different from a user's password for his or her personal account.
It is used for two things:
1. Approving a payroll.
2. Unposting a payroll after being approved.
If you've updated the Security Password and forgotten the new one, you can always reset it by following the steps here - How Do I Reset My Security Password? (For Admins).