The Invoice Status screen is where you can view existing invoice status's or add new ones. You can click the Invoice Status on this screen to edit it.
To add a new Invoice Status, just click the Add button at the top right.
Then type the Short Name of what the Invoice Status will be and add a description if necessary. Choose a Status of either Active, Closed, or Archived. Once you've done this be sure to click Save to save the new Invoice Status.
Once the Invoice Status has been added, click on it in the list of invoice status's and you will see a field called System Status. Set this to either Active or Inactive and this determines whether the current status is considered active or inactive. (The Manage Invoice screen defaults to showing only active status invoices so the System Status must be set to active for any invoice with that status to show up by default).