This encourages the growth of certain bacteria on their surface which give them distinctive flavors.
Conversely, the term "washed rind" is sometimes reserved only for the hard ones.
Washed-rind cheeses are periodically cured in a solution of saltwater brine or mold-bearing agents that may include beer, wine, brandy and spices, making their surfaces amenable to a class of bacteria (Brevibacterium linens, the reddish-orange smear bacteria) that impart pungent odors and distinctive flavors and produce a firm, flavorful rind around the cheese.
[1] Washed-rind cheeses can be soft (Limburger), semi-hard, or hard (Appenzeller).
The same bacteria can also have some effect on cheeses that are simply ripened in humid conditions, like Camembert.