How to remove an email alias?

To remove an additional address (which has different text before the'@' from the main @icloud.com address) go to the Mail page at icloud.com, click the cogwheel icon at bottom left and choose 'Preferences'. Click 'Accounts' in the pane which opens. You will see your aliases listed: click one and then click 'Delete'.

However if you mean the @me.com or @mac.com versions of the main @icloud.com address these cannot be deleted.