Family History Centers are "branches" of the Family History Library, the world's largest genealogy library, located in Salt Lake City, Utah, USA. FHCs are free facilities, usually located in a church building or occasionally in a public library. You will find knowledgeable people there, willing to offer suggestions to help you with your research. The parent organization is FamilySearch (https://www.familysearch.org/) financed by the Church of Jesus Christ of Latter-day Saints, but FHCs are open to everyone of all faiths, and you are not asked to identify your religious faith.
There are over 4600 FHCs scattered around the world. To find the ones nearest to you use this link http://www.familysearch.org/eng/library/FHC/frameset_fhc.asp
In a FHC you have access to some of the world's largest subscription databases for free!