Toxic Black Mold
Some types of mold are toxic, and some are just a nuisance. If you have mold, it's important to figure out which kind you have. Harmless mold is merely unsightly and annoying; it can be quickly cleaned with a diluted bleach solution. If it grows back, that means that the problem is more than just a surface issue. You may need to remove part of the wall where the mold is growing in order to address the problem at its source.
However, before you do this (or have a contractor do this) it's a good idea to see if the mold is toxic black mold or another harmful variety. (A mold can be any color and still cause health problems, since there are many varieties of mold and just as many individual reactions to mold.) Before disturbing the mold further, a mold test can determine if toxic black mold is present, or if another mold variety is there. Since mold danger increases as spores spread throughout the air, a big toxic black mold problem or other mold issue will need to be well-contained so that the air quality in other parts of the house isn't harmed.
A mold test done by a mold inspection professional can offer a good idea of the type and degree of mold present. This may take a while, but in the meantime you can ensure that conditions in your house don't favor mold. Use a dehumidifier to make life unpleasant for mold, since toxic black mold thrives on moisture. If the mold test reveals a serious problem, you many need to temporarily evacuate your house while it's cleaned up by a professional. Like asbestos removal, mold remediation is best left to a professional rather than to a homeowner. Increased exposure to toxic black mold spores can cause serious health problems, and any person (professional or otherwise) should wear adequate protective gear while working with it.