Mold is a type of fungus that reproduces by releasing airborne spores. Mold typically grows well in essentially any location with a warm temperature and a good supply of water, so you can develop mold in your home after a simple problem like a leak or after severe damage, like flooding. There are a wide variety of species of mold. In homes, there are a few species that you are more likely to encounter, and if you find mold growing on your drywall, it's probably one of these species.
Cladosporium colonies are olive green, brown or black, and grow on wet surfaces. Wallpaper is a common location for this mold to grow. It can aggravate allergies and asthma. Though rare, it can also cause some illnesses and infections of the skin, eyes, sinuses and brain, and this mold is considered a human pathogen. People with a weakened immune system are particularly at risk for infections caused by this mold.
Aspergillus is common in the environment, growing in the soil and on both plants and decaying organic matter. In the home, it grows on building materials like drywall, and can also be found in dust. When a person inhales the spores, they are usually destroyed by the immune system. In some cases, though, they can cause an infection known as aspergillosis. There are several types of aspergillosis infections, such as allergic bronchopulmonary aspergillosis, which causes wheezing and coughing, or invasive aspergillosis, in which the fungus damages tissues in the body, usually the lungs. These are more likely to occur in people with a weakened immune system or a condition that makes it easier for the spores to invade the body, such as a wound.
Penicillium is a mold that is actually beneficial to humans. It's used to make Roquefort and Camembert cheeses and salami sausages. It's also used to create the antibiotic penicillin and can be used as an antifungal treatment as well, as it is used to make the antifungal medication griseofulvin. It rarely causes harm to humans, though it can be an allergen. Like other molds, it tends to grow on areas that are wet or water damaged. On drywall it's likely to grow in the paper, which is full of cellulose, or on wallpaper.
Alternaria grows well on drywall and other surfaces with cellulose, like wallpaper, and doesn't need a lot of water. It's most likely to cause allergies, though it can be infectious. Like other types of mold, it typically only poses a risk to individuals with a weakened immune system or wounds. Most species of this particular mold don't grow at human body temperature, which means that a person's body heat could kill most varieties of alternaria.
Stachybotrys chartarum is greenish-black in color and grows well in places with a high cellulose content, like drywall, and needs moisture or high humidity to grow well. This mold is not as common as the others mentioned here. Stachybotrys creates toxins, and ingesting these toxins causes a disease known as stachybotryotoxicosis, but this disease is primarily found in horses. This is the mold thought by many people to be a cause of "sick building syndrome," but there is little concrete evidence to suggest that it causes this condition. This mold was also thought to cause acute idiopathic pulmonary hemorrhage among infants, but again, there is currently little evidence to support this.