Attachments are stored within the message.

The best is to backup the entire profile folder. http://kb.mozillazine.org/Thunderbird_:_FAQs_:_Backing_Up_and_Restoring

In email, an attachment is just a section of the email message, set off by unique markers so that it can be identified and treated appropriately. If it isn't plain text, then it will need to be encoded in such a way that it can be expressed in printable characters. MIME encoding and base-64 are examples of such encodings. So, inherently, attachments are part of the message. Programs that detach and store attachments separately are actually modifying your messages and it can go horribly wrong if it makes a mistake.

Thunderbird stores your messages verbatim, that is, as received. So the short answer to your question is that in Thunderbird an attachment is stored within the email message that delivered it.

In a business context, I find that most attachments are significant documents in their own right and usually deserve to be saved and filed along with related documents. Pragmatically, I'd say that the email store is marginally more fragile and less robust than the regular file system, so I'd always save valuable attachments separately from email.