If you need to find messages at a later date, you will be able to do so more easily. Your inbox is where all new messages come into and reside until they are deleted or moved to another mailbox. This is not the case. Clicking on the Inbox link without the picture of the folder will show you the email messages in the Inbox mailbox. Clicking on the link with the folder will show you any other mailboxes that you may have created in the Inbox mailbox.
All mailboxes have at least one link with a folder picture and one without.
Again, the one without the folder picture shows the messages in that mailbox. The one with the folder shows the mailboxes contained within that mailbox. In other words, if you want slightly more organization within your mailboxes, you could create a mailbox folder and have other mailboxes underneath it. Most people simply create a mailbox rather than a folder with a series of mailboxes contained within it. Even if you do only create mailboxes - you will still see the folder icon as well.