Moisture and humidity will wreak havoc in your crawl space if not properly controlled. Water should not be in there at all, especially since most of the air you breath in your home comes up from the crawl. So if there's mold on the wood, those spores will travel up through the home. The wood then will eventually start to rot, compromising the structural integrity of the home.
That's what was happening in this South Rockwood crawl space. HomeSpec had to remove the mold stains, sister the rotting joists, and encapsulate the crawl space to protect against moisture.