The inciting incident in a story is the event that takes place that causes the protagonist to take action or "get things going."  Without the inciting incident, the story would not take place; there would be no action.  The inciting incident is where the action of the story begins, and it should grab the reader's attention. This is the event that must happen in order for everything else to happen, so it should take place near the beginning of the story.

In Edgar Allan Poe's short story "The Black Cat," the reader is given a considerable amount of background information in the exposition of the story.  Then comes the inciting incident.  It takes place when the narrator recounts the events of an evening when he came home drunk and encountered Pluto, his favorite pet.

One night, returning home, much intoxicated, from one of my hauints about town, I fancied that the cat avoided my presence.  I seized him; whe, in his fright at my violence, he inflicted a slight wound upon my hand with his teeth.  The fury of a demon instantly possessed me...I took from my waistcoat-pocket a penknife, opened it, grasped the poor beast by the throat, and deliberately cut one of its eyes from the socket!

Had the narrator and protagonist not come home inebriated and cut out the cat's eye, he would not have become obsessed with the cat's behavior or murdered his wife when the she interfered in his attempt to hit the cat with his axe.  The plot would not have taken place.