Incidences is technically a real word, but it is often misused and is rarely called for. Those who say "incidences" usually mean "incidents."
An incident is a single event or episode: An incident of food poisoning was confirmed and investigated.
Incidence is the rate at which something happens, usually something bad: The incidence of diseases transmitted by food has decreased.
Sometimes the words can overlap. When incidents of crime are occurring with some regularity, there is an incidence of crime in the vicinity.