Stains are rarely ever a good thing. The only things that look nice with stains are stylized flooring and glass. Seeing them appear randomly, however, can be a bad thing. This is especially true with water damage and stains that they produce. Usually, a brown, spreading splotch is signs of water damage and it needs to be dealt with immediately.
If you leave it be, it can produce mold and mildew, giving the area a disgusting smell and the possibility of health problems. You can replace the areas if it’s cracking or chipping off, but if you can dry it well enough, you can also paint over it.
The brown stain will remain there even if you dry it. Air flow and heat is important to get it to that state. Make sure that it is all dry by feeling it and make sure to sanitize it with bleach or Clorox or some other antimicrobial liquid.
After you sanitize it from the mold and have it dry further, you can paint over the brown, discolored area with the same color as the rest of your wall. If you don’t make sure it’s dry, though, it can still ruin the new coating of paint! There is more information on this guide: http://www.damagecontrol-911.com/how-to-cover-water-damage-with-paint/