Windows Live Mail will keep using the last password you supplied, regardless of what you may have changed at the email provider's level. In most cases, you'll get a "Please enter your user name and password for the following server
" error message and login form (see screenshot). If that's the case, changing password is as easy as typing the new password over the old one, optionally allowing Windows Live Mail to "Remember Password", and clicking OK! But this tutorial will show you how to change email password at the account level, including when two different passwords are used for incoming and outgoing mail servers.
Note: changing password in Windows Live Mail will not affect your email account itself. To set a new password, you'll need to reset it with your email provider first, and then only can you update it inside Windows Live Mail.
Caution: email passwords are nearly always "case-sensitive" (uppercase and lowercase letters considered different characters). A wrong capitalization will mean a wrong password, so make sure that CapsLock is turned off :)
If you only have a single email account currently setup in Windows Live Mail, select the "Accounts" tab in the Ribbon, and click on the Properties button: 
If you have multiple email accounts setup in Windows Live Mail, click on the File button (top left corner), select "Options", and click on "Email accounts". When the Accounts dialog opens, double-click on the email account whose password you want to change: 
Either way, click on the Servers tab of the account property window: under Incoming Mail Server, erase the old password and type the new one inside the Password text field. (Optionally check or keep checked the "Remember password
" checkbox, so you don't have to re-enter it whenever Windows Live Mail sends or receives messages. 
Tip: you can skip this step if you're using one of these webmail providers (which use the same password everywhere) - AIM / AOL Mail, Gmail, iCloud Mail, MSN / Live.com / Hotmail / Outlook.com (Microsoft), Yahoo Mail, or Zoho Mail.
In most cases, your email password is the same for the incoming and outgoing mail server (send / receive settings). To double-check that, click on the Settings button under Outgoing Mail Server . When the corresponding dialog opens, make sure that "Use same settings as my incoming mail server
" is selected: if it is, you don't need to do anything! Otherwise, change the outgoing password as well, and click OK to save it. 
Tech note - incoming and outgoing mail server passwords can be different for primarily two reasons: security, and load balancing. To keep things simple for users, however, username and password are generally the same.
Click OK to apply, and click OK once more to return to your emails. (And you can click on the "Close" button to dismiss the account listing window if it was open.)