I'm not sure which of the two common questions you're asking Jory.
Do you want to erase all of the emails in the account or do you want to also close the account?
The problem with many free email accounts is that there's no way to close them. For some reason the providers haven't thought that would ever be necessary. If you just go in and delete all of the email, that doesn't stop any new mail from coming in. If you're worried that someone else has access to your account, perhaps the best thing to do is to change the password and THEN erase all the mail. That way it's unlikely that anyone will ever be able to log on and read the mail.
Erasing the existing mail is usually quite easy. In most cases you can simply select all the messages and hit the Delete button on the email site.
Of course you should check the Help page on the email site because they may have provided you with a way to unsubscribe.
Paul Zucker