I left a mattress directly on a hardwood floor, and some mold grew underneath. There is no insulation in the crawlspace beneath the floor, so the temperature differential between warm bodies sleeping on the mattress and cold air under the floor resulted in condensation between the mattress and the floor, which is a perfect place for mold to grow.
Mildew can also grow under potted plants and carpet, against uninsulated walls, in damp basements, if you have a water leak, or even under wet laundry left sitting too long.
Step 1: Try Wiping Up the Mold
The mildew growing on the intact polyurethaned surfaces wiped up so quickly that I didn't get a picture of it before we cleaned it up.
Step 2: Sand the Floor
In the images, you can see that I tried removing the mold with steel wool. That was unsuccessful, so I sanded. If you use steel wool, be sure to clean all steel fibers up as any left may rust.
Step 3: Remove Dust
Step 4: Refinish Hardwood Floor
If you use a cheap hog-bristle brush as I am in the images, be sure to remove any loose hairs before you start applying poly so those hairs don't come out and get stuck in the poly.
The floor was originally finished with an oil-based polyurethane, so I didn't expect the refinished areas to match exactly. However, they're normally out of sight (why mold grew there in the first place), and my objective was to seal-out further moisture rather than perfect them cosmetically. If this is a more visible area, test your polyurethane and consider applying a light stain. If the appearance really matters, you should probably refinish the entire floor.
I made sure mold wouldn't be a problem again in the future by building a low-profile bed frame.