Why is the iPhone mail asking for a password for the Description of the account

Are you trying to set up the mail account manually, as described here, and in this picture?

...

How to set up your email account manually

If you need to set up your email account manually, make sure that you know the email settings for your account. If you don’t know them, you can look them up or contact your email provider. Then follow these steps:

1. Go to Settings > Mail, then tap Accounts.
2. Tap Add Account, tap Other, then tap Add Mail Account.
3. Enter your name, email address, password, and a description for your account. 
4. Tap Next. Mail will try to find the email settings and finish your account setup. If Mail finds your email settings, tap Done to complete your account setup.

...

If yes, the field "Description" needs no password. It is just the name you choose yourself, in case you have multiple mail accounts.

The password is the password for the mail account, not for the description you fill in.