The most basic answer is moisture, food sources, and the correct temperature.
There are mold spores throughout your home all the time. Most are microscopic and never cause an issue unless you are an individual that is highly susceptible to allergies, respiratory problems or other health issues.
When water damage occurs, (and it is not properly dried by a professional restoration company) or relative humidity is higher than +/- 65% for an extended period of time, mold growth is bound to become an issue.
Some individuals find irritation at very low levels of contamination, while others can live in severe conditions without much of the appearance of problems. At some point though, everyone is going to have some type of reaction to high levels of airborne mold spores or physical contamination.
There are many companies that tout a quick and easy remedy for mold contamination.
BEWARE! Spraying, fogging, over the counter “mold solutions” do not work and in most cases cause more problems than before by spreading spores over greater surfaces and areas.