I just want to know what a QBFC is
It's a COM library builds XML requests that QuickBooks can understand using objects. It also wraps some other QuickBooks COM components that allow you to send those XML requests to QuickBooks so that QuickBooks can process them.
and how it works in relation to post invoices and Purchase Orders from a third party program to QuickBooks
Pretty much explained it above... there are 300+ pages of documentation about this in the QuickBooks SDK. If you need specific code examples, there are numerous examples included in the QuickBooks SDK.
and which QBFC version should I use with QuickBooks 2008
Always use the latest version of QBFC. It's backward compatible with old versions of QuickBooks.