An incident refers to a particular happening, sometimes criminal but always noteworthy. If there was a food fight in the cafeteria, an e-mail might be sent to the parents of all students telling of the incident at school.
The word incident is quite vague. It can refer to a humorous occurrence or a violent one, something that disturbed one's routine or something unusual that happened. If a child screams in a library, it's not that unusual, but if an adult does, that's an incident! As an adjective, incident is used in the field of physics to describe particles or radiation that fall on a surface. The incident light showed how dirty the windows were.