How to change an email password

Changing your password is done on the internet providers website. You will then need to update the password in your Mail Settings. When updating the password in Mail, you will need to provide it in to locations, the first one is for incoming email (POP/IMAP) and the second location is for sending the email and is called SMTP.

If you need help with updating the password in the Mail application after changing it on you email providers website, then feel free to reply with the OS version and someone will be able to guide you on doing that. In general, for the Mac it is at Mail > Settings > Accounts > Server Settings.

Which email password? I have 2 accounts on my computer and none of them are from Apple.

Exactly how you change your iCloud email password (and in fact the password for your entire Apple ID) depends upon if this is an adult or a child, and the equipment you have. Click on this link to learn how to change your Apple ID password --> Change your Apple ID password - Apple Support