Can you explain what 'The other folders on my mailbox' means?

With POP Thunderbird can only access Inbox on the server. Any other folders you'd need to create locally on your computer.

If there are other existing folders on the server, you'd need to set up your account as IMAP in order to see them in Thunderbird.

There are other folders in my mailbox aside from the Inbox and trash (not sub-folders). It appears in my webmail but not on my Thunderbird account.

So the answer is to use IMAP. http://kb.mozillazine.org/Convert_a_POP_account_to_a_IMAP_account