The purpose of the New App screen is to allow the administrator to invite applicants to apply via mathjobs. This is usually done when an application arrives on paper. Clicking on the "NewApp" link will bring up a window with the No Cover Sheet Form similar to the one below.
Here you can add applicants that are not already on your application List. They could be new applicants that are not in the database, or the applicant could already be in the database but doesn't show up on your application List because they haven't applied online for any of your jobs yet.
After you add an applicant here, they will appear on your application noCover list. You could also click on the application noCover link in the header first to see who is currently on the list.
Aside from basic name and email information, you will need to provide the following on the No Cover Sheet Form:
To the far right of Email Address is a checkbox with Email?. The checkbox is for emailing the applicant being entered. If the checkbox is checked, the applicant will receive an email, asking that they login and enter an AMS coversheet.
This last section is Jobs applied for. Each of your department's job listings in the database will be here, with a checkbox at the left. Click to check off the position(s) that the candidate is applying for.
Click on the Submit button to add the applicant to the noCover list.