A FHC is an abbreviation for Family History Center. "Family History Centers are branch facilities of the Family History Library in Salt Lake City. Centers provide access to most of the microfilms and microfiche in the Family History Library to help patrons identify their ancestors. Everyone is welcome to come to the centers and use Family History Center resources." To read more, follow this link to the Familysearch.com site.
Sometimes records are held in the center, but more often they will be obtained on loan from the main library, and a small fee will be charged. Once the film is delivered to your local FHC, you will be able to use their facilities to view the film. You can often also make photo-copies, again for a nominal charge.
The centers are manned by knowledgeable volunteers, who will guide you through the necessary steps to ordering a film or fiche.
Before heading out the door, check first to see if you require an appointment. Some FHCs require one, while others welcome walk-in researchers during stated hours of opening.
To find a library close to you, visit Familysearch.com.