A IMAP folder will be displayed in italics if the folder has a \Noselect flag. Normally this means the folder can contain child folders, but not messages.
This most commonly occurs if you use the default settings for the IMAP server directory in Account Settings > your account > Advanced button for a Gmail IMAP account (the [Gmail] folder).
A "mailbox" is IMAP-speak for what a lot of other software calls a folder or mail folder. IMAP uses different terminology because it's only meant to refer to a named object that can contain messages. It doesn't have to be able to also include other mailboxes. If the object has a \NoSelect flag it is not a mailbox and should not be able to be subscribed.
A "dual-use name" (or "dual use mailbox") is one that can contain both messages and mailboxes. Some email clients need to be told whether an IMAP server does or does not support dual-use names. That's why Postbox has a "Server supports folders that contain sub-folders and messages" checkbox in Account Settings > Advanced.
At times you may run across a situation where folders are subscribed but don't exist anymore. Indeed, if you turn on Postbox's IMAP logging, you will see them listed as (\Subscribed \NonExistent).
There are a few ways to address these folders:
1) The first solution to get rid of those folders is surprisingly simple: re-create them, then you can delete them. Go the parent folder, and for every phantom subfolder create a new subfolder of the same name. As you do that, the folder's appearance will change from grey italic back to normal again. After verifying that the folders are empty, you can delete them and they will be gone entirely.
2) Another cause could be that the folder is not subscribed to, but it does contain sub-folders that are subscribed to. To fix this, subscribe to the folder by going to the File menu > Subscribe > select the account > then select the folder and subscribe to it. Restart Postbox after this is done to reset the folder list.
3) Contact your mail provider and have the folder unlocked, or deleted if the folder is empty and no longer needed.