Reading through the white-paper cleared up a lot of questions I had.

Basically, the Bitcoin blockchain simply can't handle very large data entries - so the Factom P2P network and blockchain handles larger entries which are then hashed into the Bitcoin blockchain.  So, Factom is a layer on top of the Bitcoin blockchain.  The two chains become intertwined which strengthens both of them. Factoids are tokens that are spent in the process of entering information into Factom.  They serve as anti-spam and they also serve as a way to reward the federated servers.

Factom can operate on top of any blockchain - but they have chosen to use the Bitcoin blockchain.  Kudos to them