So, none of the responses from Apple were helpful. This was from another site, and it worked.
Aol Desktop
It was step 6 that did the trick. Pretty jive that you can enter that password in all the other places, and it didn't work. Pop-ups were popping up all over the place--I would enter the password every time something popped up-- entering it in the Accounts Information field in the Preferences for Mail, quitting and restarting Mail, and nothing helped. I spent 2 hours with Apple support one day, and a half hour on another day. They seemed helpless. Does this really need to be so difficult? The fix seemed very simple. Dear Apple Support personnel: Please check it out and add it to your data base! It may not work for all, but it sure worked for me. The field for password in the 'Advanced' area of the 'Edit SMPT Server List' was blank. Everything had been working fine up until it suddenly stopped working. Email was still completely functional on my phone and on the AOL website. Just not in the Mac Mail application. But step 6 below fixed it.
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Go back to the Mail app Preferences by pulling down the Mail menu and choosing “Preferences”
Select the “Accounts” panel from preferences window
Choose the mail account that is throwing password errors
Under the ‘Account Information’ tab, click on “Outgoing Mail Server (SMTP)” and choose “Edit SMTP Server List”
Click the ‘Advanced’ tab
Be sure the email username is entered properly here, then click into “Password” and enter the correct email password associated with the account
Click “OK”, then close out of Preferences and choose “Save” when requested
Send email again, it should now work as intended
Mac Pro, OS X El Capitan (10.11.6)
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Mail User Guide
Use the Mail app to send, receive, and manage email for all of your email accounts in one location. Simply add the accounts—such as iCloud, Exchange, Google, school, work, or other—you want to use in Mail.
Add an email account
The first time you open the Mail app on your Mac, it may prompt you to add an account. Select an account type—if you don’t see your type, select Other Mail Account—then enter your account information.
If you already added an email account, you can still add more. In Mail, choose Mail > Add Account, select an account type, then enter your account information. Make sure the Mail checkbox is selected for the account.
If you’re using an account on your Mac with other apps, such as Contacts or Messages, you can also use that account with Mail. In Mail, choose Mail > Accounts to open Internet Accounts preferences, select the account on the left, then select the Mail checkbox on the right.
Temporarily stop using an email account
In the Mail app on your Mac, choose Mail > Accounts.
Select the account, then deselect the Mail checkbox.
Now the account’s messages are not shown in Mail.
To use the account again with Mail, select the Mail checkbox; the account’s messages are shown again (they don’t need to be downloaded from the server again).
Remove an email account
When you remove an email account from Mail, the account’s messages are deleted and no longer available on your Mac. Copies of messages remain on the account’s mail server and are still available (from webmail, for example).
Important: If you’re unsure whether messages you want to keep are still on the mail server, move or copy them to a mailbox stored on your Mac (the mailbox appears in the On My Mac section in the Mail sidebar) before you delete the account in Mail.
In the Mail app on your Mac, choose Mail > Preferences, then click Accounts.
Select an account, then click the Remove button .
Note: If the account is used by other apps on your Mac, you’re asked to remove the account in Internet Accounts System Preferences. Click the button to open Internet Accounts, then deselect the Mail checkbox for the account. To stop using the account in all apps, make sure the account is selected, then click the Remove button .
See alsoUse SSL to connect to the outgoing mail server in Mail on MacView email account information in Mail on MacFree up storage space for email accounts in Mail on Mac