I only heard about this for the first time yesterday, and based on the information I had to go on at that time, I was deeply upset. Since then, I have talked to a number of sources about "No Match, No Vote" and feel quite a bit relieved by what I've learned.

The Voter Registration Verification (so-called "No Match, No Vote") Law aims at preventing voter fraud and ensuring the integrity of ballots cast in the state of Florida. It involves matching various pieces of voter identification (driver's license, social security card, etc.) with existing information in various state databases.

There seems to be a great deal of misinformation circulating about the law, like "if the address on your license or ID card doesn't match the address on your voter registration card, then you can't vote." This is false.

Check out this press release from the Florida Department of State, which reads like a sort of FAQ.
http://www.dos.state.fl.us/news/communications/pressRelease/pressRelease.cfm?id=330