Ground Fault Circuit Interrupter. A personnel protection device used to prevent electric shock hazards. Typically used in wet locations on stage or in areas required by the NEC (your kitchen and bathroom are but two examples). GFCI's must meet the UL943 standard and must trip below 6ma of fault current. GFCI's are 60Hz-only units for use in North America. Similar protection is provided in 230V/50Hz markets by RCD (Residual Current Devices) that trip at 30ma. RCD's cannot be used for personnel protection in the US or Canada.
Normal GFCI's cannot be used on the output of dimmers, This application requires a special Dimmer GFCI, such as the 36895 from Leviton. There are, however, GFCI Dimmers available from at least one major dimmer manufacturer. These have the GFCI circuit embedded in the dimmer, and the entire unit is Listed to UL943. Some manufacturers of portable power distributions make GFCI units.
GFCI's can be subject to nuisance tripping, especially on long cable runs.
A GFCI should not be confused with a GFP (Ground fault Protector) which is a device with a much higher trip current suitable only for equipment protection, not personnel protection.
Note: There is no such thing as a GFI, it is a common misnomer for a GFCI.
Some well-known GFCI manufacturers who make devices suitable for the entertainment industry are Bender, Leviton and Littelfuse K-Tec. GFCI dimmers are available from ETC.
The definitive text on GFCI's is "Overcurrents and Undercurrents" by Earl W. Roberts. It is available here, among other places on the web: http://www.ais-engineering-books.com/books/pc/viewPrd.asp?idproduct=265
See also http://www.controlbooth.com/forums/glossary/11237-ground-fault-protection-primer.html.