This option lets you sign the database with your current ID. In this situation, signEZ does not prompt for your password since it does not need to switch ID.
You can save your own password so that when signEZ switches back to your ID it will not prompt you for your own password. The password is stored in a profile document in the signEZ database and is encrypted. You can click on Delete password to remove it from the signEZ database.
Lotus Notes may prompt for your password if you are working on a database on a server.