Often, it happens when you wish to decide an email account for some reason. To do that, unlock your windows phone and go to Settings (by swiping to right). Then go to “Email and Accounts” and then tap and hold on the account you wish to delete. From the pop up menu, select “Delete”. Another thing to note is that you cannot delete the default windows live account, unless factory reset the windows phone.

Keep in mind that when you delete an email account, you delete all the emails from your phone (not from the server, of course). This includes the unsent drafts as well. You also delete every single custom setting you had with that account. The next time you set up that account, you will have to customize the settings again.