
A mailbox is a location on our servers where it can store e-mails. Think of a mailbox like your postbox - in order to accept mail from the postman, you need a postbox. It's the same with a mailbox - in order for the server to receive e-mail for you so that you can either read it (if you're using IMAP) or download it (in the case of POP) later, you need to create an account with a mailbox.
In most situations, yes. If you want to receive e-mail from other people, you will need a mailbox on your account. However, there are two exceptions when you won't need a mailbox: