Removing an email address or email account is a fairly easy task. However, there are a few things you should be aware of before completely deleting any account. Mainly, if you are using IMAP as your email protocol, then all of your stored messages will be deleted as soon as you remove the account from cPanel.
If you are removing the account simply to rename it or change the email address, then make sure you have a backup of all the messages on the server in a local folder, as they will all be deleted once the account is removed.
Here is a demo video on how to delete an email address in your cPanel hosting account.