They are soft and the rind is covered with white mold, usually Penicillium Candidum or Penicillum Camemberti, but usually Geotrichum Candidum is blended in to reduce the growth of the Penicillium. The cheese is matured from a week or two up til a couple of months, with an average of four weeks, I would say. The fresh varieties have a whitish firm core, while maturation leads to the cheese being soft right through. Over-mature cheeses smell of ammonia and should not be eaten, even though they are probably not harmful. Most famous of the bloomy rind cheeses are of course Brie and Camembert.
Cheeses with a bright white rind are usually industrially made, while those with red/brown spotted rind are made by artisans.