What does the "visibility" number mean on an approach plate?
If this question is about the US, the FAA's Chart User's Guide is a useful source for questions about approach plates or any other charts. It says:


  This section gives the pilot the lowest altitude and visibility
  requirements for the approach. There are two types of landing
  minimums: Straight-in landing or Circling. Straight-in landing
  minimums are the MDA and visibility, or DH and visibility, required
  for a straight-in landing on a specified runway. Circling minimums are
  the MDA and visibility required for the circle-to-land maneuver.


And:


  The visibility values are shown after the DA/DH or MDA. They are
  provided in statue [sic] miles or runway visual range (RVR). RVR is reported
  in hundreds of feet. If the visibility is in statute miles, there is
  an altitude number, hyphen, whole or fractional number, e.g. 530-1.
  This indicates 530 feet MSL and 1 statute mile of visibility. The RVR
  value is separated from the minimum altitude with a slash, e.g.,
  1540/24. This indicates 1540 feet MSL and RVR of 2400 feet.


The number is indeed a limitation: if the required visibility doesn't exist then the pilot can't use the approach. However, there are some differences in what that really means depending on the type of flight: an airline flight (part 121) can't even start an approach if the reported visibility is less than the approach requirements; a private flight (part 91) can start an approach but may not land if the flight visibility is below minimums. This question might be relevant.