A fixed bridge doesn't move. A Floyd Rose (or any other tremolo bridge) is mounted on posts, with springs underneath that allow the bridge to pivot when you use the whammy bar. A fixed bridge, such as the style on a Les Paul or Telecaster, is screwed down or "fixed" to the guitar's body, and doesn't move. A fixed bridge will have better tuning stability because it doesn't pivot, but of course you can't use a whammy bar, and most fixed bridges don't have the fine tuners that a Floyd Rose has.
A Floyd can be "blocked off" so that it doesn't pivot on its mounting posts, but still has the benefit of fine tuning. It takes less time to restring a fixed bridge. So, do you need to use the whammy bar? Do you care about fine tuners? Those are deciding factors.