NFA stands for the National Firearms Act.
The Act is a federal statute which imposes a statutory excise tax on the manufacture and transfer of certain firearms (such as gun suppressors, gun silencers, SBRs and machine guns) and mandates the registration of those firearms.
Useful NFA Links
Yes, citizens of Florida can own silencers and suppressors legally here. In September 2014, the Florida Fish and Wildlife Conservation Commission is set to consider a proposal to legalize the use of gun silencers, for hunting certain game.
The terms “suppressors” and “silencers” are used interchangeably. Both the United States Department of Justice and the ATF (Bureau of Alcohol, Tobacco, Firearms and Explosives) refer to suppressors as silencers.