Every day, people breathe in Aspergillus spores with no adverse issues. But this mold can be a problem for those at high risk or with weakened immune systems.
Molds are made of many cells. While you can see some with the naked eye, a microscope will show root threads that grow into the food, a stalk rising above the food, and spores that form on the ends of the stalks. The colors of mold are the spores. The roots can grow deep into the food. So what you see on the surface is not the entire mold.
In the case of home canning, the water bath processing method will easily destroy mold on high-acid foods when processed properly. But if any seal defect is present, air and contaminants can get inside the jar and cause spoilage.
More information can be found in Molds on Food: Are They Dangerous?