If FIM Synchronization Service is the heart pumping information, FIM Service is the brain (sorry FIM CM, but your brain is not as impressive; I'll give you credit later).
FIM Service plays many roles in FIM, and during the design phase the capabilities of FIM Service is often on focus. FIM Service allows you to enforce the Identity Management policy within your organization and also make sure you are compliant at all times.
FIM Service has its own database, where it stores the information about the identities it manages.