What is the black mold that grows in bathrooms and basements
 
There are a number of mold types/genera that are either black or gray in color or produce black pigments on the substrate that they are growing on. These include Cladosporium, Pithomyces, Stemphydium, Ulocladium, Aureobasidium, Alternaria, Memmoniella, and Stachybotrys. Stachybotrys and Memnoniella are the only black mold types that are known to produce mycotoxins, which produce a potential exposure hazard when infested materials are disturbed. Stachybotrys and Memnoniella infestations typically only occur on repeatedly wetted materials that contain cellulose. These include the paper on gypsumboard, cardboard, ceiling tile, cellulose insulation, wood, etc. If the black mold is growing on materials that do not contain cellulose, it is unlikely that either Stachybotrys or Memnoniella are present.

As you question suggests "black mold" growths are common in houses particularly in bathrooms and some materials in basements. The black mold that you may see growing on shower walls, and grouting on showers and bathtubs is unlikely to be Stachybotrys or Memnoniella. The food source in these cases is likely to be the film of soap that gradually builds up in these locations. Black mold can often be seen growing on painted ceilings above bathtub/showers as well as on shower curtains. Since these materials do not contain cellulose they are unlikely to be infested with Stachybotrys or Memnoniella.

The most common black mold found in "black mold" growths is Cladosporium. It is not known to pose any toxic hazard. It is the most common mold type found in air samples collected both indoors and outdoors. As such we are likely to be exposed to it all the time. Exposures to high levels of Cladosporium pose a risk of developing allergy or even asthma in highly sensitive individuals.

Other mold types, which may be present in "black mold" spots, include Ulocladium, Stemphylium, Pithomyces, Alternaria, Dresclera, and Aureobasium. None of these genera are known to produce mycotoxins, which cause a toxic hazard on exposure.

How can one get rid of a black mold infestation? That depends on the type of infestation it is, its size and location. Black mold growing on bath walls & ceilings can be treated with bleach (a cup to a gallon), and washed with a strong detergent. Walls & ceilings can be then repainted. Though the bleach will kill the mold, it may not remove the black pigment associated with it.

If black mold is growing on materials containing cellulose it is prudent not to disturb them until they are shown not to contain toxic mold types (see other Stachybotrys articles under the search function on this page). Samples can be taken with transparent sticky tape and analyzed by a laboratory providing microbiological analytical services.

If a black mold infestation on cellulose-containing materials proves negative, remove and discard (carefully) infested materials into heavy-duty plastic bags. Even exposures to non-toxic mold types poses a health risk (allergies and asthma), so that any mold related work should be conducted to minimize exposure to yourself & your family.