Family History Centers (FHC) are satellite branches of the Family History Library (FHL) in Salt Lake City, the largest genealogy library in the world.
To locate a FHC near you, click here.
Although FHC are generally located within LDS Churches, they are open to anyone and proselytizing is not allowed.
Most centers have a separate entrance, or a back entrance separate from the main church entrance.
These centers are staffed with volunteers who have typically been doing genealogical research for decades.
FHC also has subscriptions to the major genealogical websites and allows you to access them for free.
You can search the FHL catalog online here.