When a member joins using the Lyris web interface, Lyris can ask the person to pick a personal password. A personal password is useful for mailing lists where security is important. If no password is defined for a user, then other people can enter the web interface as that person by typing in their email address. Requiring each user to have a personal password adds considerable security to your mailing list.
This option allows you to require a password, to make the password optional, or to not ask for a password at all.
Note that if joining by email is allowed, that this setting has no impact, because there is no way to require a password from people can join by email. If you want to always have member passwords, you should also set your mailing list to not allow joining by email, so that people must use the web interface to join. See Allow Joining by Email.